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While this is on the front page, Recoltes -> Récoltes; title of MacPherson article; link to other answer
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This answer addresses your second question, regarding the specific case of SGA 5. In short: the contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2". Also, see my other answeranswer about the original Exposé.

According to Grothendieck's "Recoltes"Récoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

About the lost exposés:

  • There was a group of introductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and I don't know where they ended up. I personally think they are in the Grothendieck Archives (Cote nº33) You can read more about them herehere.
  • Exposé II, as I said earlier, was reworked by Deligne and included in his volume about Étale Cohomology. The original exposé is kept at the IHÉS and can be read online (see my other answeranswer).
  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to ReSRéS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite GroupsLinear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to Grothendieck, who somehow lost it.
  • There was also a last exposé about open problems, which Grothendieck talks about in ReSRéS and which notably contained a conjectural "discrete Riemann-RochRiemann–Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPhersonMacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne in SGA 4 1/2.

This answer addresses your second question, regarding the specific case of SGA 5. In short: the contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2". Also, see my other answer about the original Exposé.

According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

About the lost exposés:

  • There was a group of introductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and I don't know where they ended up. I personally think they are in the Grothendieck Archives (Cote nº33) You can read more about them here.
  • Exposé II, as I said earlier, was reworked by Deligne and included in his volume about Étale Cohomology. The original exposé is kept at the IHÉS and can be read online (see my other answer).
  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to Grothendieck, who somehow lost it.
  • There was also a last exposé about open problems, which Grothendieck talks about in ReS and which notably contained a conjectural "discrete Riemann-Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne in SGA 4 1/2.

This answer addresses your second question, regarding the specific case of SGA 5. In short: the contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2". Also, see my other answer about the original Exposé.

According to Grothendieck's "Récoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

About the lost exposés:

  • There was a group of introductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and I don't know where they ended up. I personally think they are in the Grothendieck Archives (Cote nº33) You can read more about them here.
  • Exposé II, as I said earlier, was reworked by Deligne and included in his volume about Étale Cohomology. The original exposé is kept at the IHÉS and can be read online (see my other answer).
  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to RéS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to Grothendieck, who somehow lost it.
  • There was also a last exposé about open problems, which Grothendieck talks about in RéS and which notably contained a conjectural "discrete Riemann–Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne in SGA 4 1/2.
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This answer addresses your second question, regarding the specific case of SGA 5. In short: the contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2". Also, see my other answer about the original Exposé.

According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

About the lost exposés:

  • There was a group of introductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and I don't know where they ended up. I personally think they are in the Grothendieck Archives (Cote nº33) You can read more about them here.
  • Exposé II, as I said earlier, was reworked by Deligne and included in his volume about Étale Cohomology. The original exposé is kept at the IHÉS and can be read online (see my other answer).
  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to Grothendieck, who somehow lost it.
  • There was also a last exposé about open problems, which Grothendieck talks about in ReS and which notably contained a conjectural "discrete Riemann-Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne in SGA 4 1/2.

This answer addresses your second question, regarding the specific case of SGA 5. In short: the contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2". Also, see my other answer about the original Exposé.

According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

About the lost exposés:

  • There was a group of introductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and I don't know where they ended up. You can read more about them here.
  • Exposé II, as I said earlier, was reworked by Deligne and included in his volume about Étale Cohomology. The original exposé is kept at the IHÉS and can be read online (see my other answer).
  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to Grothendieck, who somehow lost it.
  • There was also a last exposé about open problems, which Grothendieck talks about in ReS and which notably contained a conjectural "discrete Riemann-Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne in SGA 4 1/2.

This answer addresses your second question, regarding the specific case of SGA 5. In short: the contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2". Also, see my other answer about the original Exposé.

According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

About the lost exposés:

  • There was a group of introductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and I don't know where they ended up. I personally think they are in the Grothendieck Archives (Cote nº33) You can read more about them here.
  • Exposé II, as I said earlier, was reworked by Deligne and included in his volume about Étale Cohomology. The original exposé is kept at the IHÉS and can be read online (see my other answer).
  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to Grothendieck, who somehow lost it.
  • There was also a last exposé about open problems, which Grothendieck talks about in ReS and which notably contained a conjectural "discrete Riemann-Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne in SGA 4 1/2.
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EDIT: This answer addresses your second question, regarding the specific case of SGA 5. In short: Exposé II is tothe contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2""SGA 4 1/2". Also, see my other answer about the original Exposé.

According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

Precisely, there were threeAbout the lost exposés:

  • Exposé XIThere was called "Computationa group of local terms" or something like thatintroductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and was substituted by exposé III-bI don't know where they ended up. You can read more about them here.
  • Exposé IXII, as I said earlier, was reworked by Deligne and included in his volume about Serre-Swan modulesÉtale Cohomology. The original exposé is kept at the IHÉS and was published elsewhere by Serrecan be read online (Linear Representations of Finite Groupssee my other answer).
  • Exposé XIII was deleted.

Also, important points remarked by Grothendieck in the oral seminar were suppressed in this edition. It's a real pity, and probably the only way to recover the lost ideas would be to find Grothendieck's original notes (probably the archives at Montpellier University contain them or the IHES library).

EDIT: More about what was missing from SGA 5:

  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.

A related theme covered by Grothendieck was "The homology class associated with a cycle". This was discussed throughout many exposés in the seminar, but is absent from the published book. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.

  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé IIXI was called "Computation of local terms" or something like that, as is known from the introductionand was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to SGA 5Grothendieck, who somehow lost it.
  • There was reworkedalso a last exposé about open problems, which Grothendieck talks about in ReS and which notably contained a conjectural "discrete Riemann-Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne and included in SGA 4 1/2 as well.

EDIT: This answer addresses your second question, regarding the specific case of SGA 5. In short: Exposé II is to be found in Deligne's "SGA 4 1/2".

According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

Precisely, there were three lost exposés:

  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups).
  • Exposé XIII was deleted.

Also, important points remarked by Grothendieck in the oral seminar were suppressed in this edition. It's a real pity, and probably the only way to recover the lost ideas would be to find Grothendieck's original notes (probably the archives at Montpellier University contain them or the IHES library).

EDIT: More about what was missing from SGA 5:

  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4.

A related theme covered by Grothendieck was "The homology class associated with a cycle". This was discussed throughout many exposés in the seminar, but is absent from the published book. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.

  • Exposé II, as is known from the introduction to SGA 5, was reworked by Deligne and included in SGA 4 1/2 as well.

This answer addresses your second question, regarding the specific case of SGA 5. In short: the contents of SGA 5 Exposé II can be found in Deligne's "SGA 4 1/2". Also, see my other answer about the original Exposé.

According to Grothendieck's "Recoltes et Semailles", SGA 5 was totally butchered by Illusie, in a combined effort with Deligne so that it looked useless in comparison with SGA 4 1/2 (which wasn't a true seminar, and stole some of the missing exposés from SGA 5). This is also the reason why SGA 5 was the last to be published.

About the lost exposés:

  • There was a group of introductory exposés about the relations of SGA 5 to other contexts and about the philosophy of six operations. Illusie had them, but he sent them to Grothendieck and I don't know where they ended up. You can read more about them here.
  • Exposé II, as I said earlier, was reworked by Deligne and included in his volume about Étale Cohomology. The original exposé is kept at the IHÉS and can be read online (see my other answer).
  • Exposé IV, about "The cohomology class associated with a cycle", was going to be redacted by Deligne, who instead included it in SGA 4 1/2, chapter 4. This theme also included an étale version of homology, with a formalism about the homology class associated to a cycle. According to ReS, these ideas were published by Verdier in an article with the same name. You can read it here: Verdier, Jean-Louis, Classe d’homologie associee à un cycle, Astérisque 36–37, 101–151 (1976). ZBL0346.14005.
  • Exposé IX was about Serre-Swan modules and was published elsewhere by Serre (Linear Representations of Finite Groups). This one was published by the IHÉS and can be found in some libraries.
  • Exposé XI was called "Computation of local terms" or something like that, and was substituted by exposé III-b. Apparently, Bucur wrote it and sent it to Grothendieck, who somehow lost it.
  • There was also a last exposé about open problems, which Grothendieck talks about in ReS and which notably contained a conjectural "discrete Riemann-Roch theorem", later referred to as "Grothendieck-Deligne conjecture" and studied by MacPherson. He also mentioned a trace formula modulo $p$, which was treated by Deligne in SGA 4 1/2.
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