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Added link to Grothendieck's paper
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David Roberts ♦
David Roberts ♦
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Hi,

I've read some discussions of Grothendieck's famous Tohoku PaperGrothendieck's famous Tohoku Paper, and I understand that one reason it was a landmark paper was that it introduced abelian categories and gave us sheaf cohomology as a certain type of derived functor. However, I've heard from various sources (Manin's Homological Algebra, my prof, and the 2 part AMS Notices articles) that one of the famous aspects of this paper is that it "reinterpreted" the basics of combinatorial topology. Does anybody know what this means? Slightly more specific: how was combinatorial topology understood at that time and how did the Tohoku paper force a reinterpretation of the conventional concepts? I know this question might be a bit ill posed, but I'd like to know if somebody understands what this means and can explain it at a first year graduate student level.

Thanks, Ben

Hi,

I've read some discussions of Grothendieck's famous Tohoku Paper, and I understand that one reason it was a landmark paper was that it introduced abelian categories and gave us sheaf cohomology as a certain type of derived functor. However, I've heard from various sources (Manin's Homological Algebra, my prof, and the 2 part AMS Notices articles) that one of the famous aspects of this paper is that it "reinterpreted" the basics of combinatorial topology. Does anybody know what this means? Slightly more specific: how was combinatorial topology understood at that time and how did the Tohoku paper force a reinterpretation of the conventional concepts? I know this question might be a bit ill posed, but I'd like to know if somebody understands what this means and can explain it at a first year graduate student level.

Thanks, Ben

I've read some discussions of Grothendieck's famous Tohoku Paper, and I understand that one reason it was a landmark paper was that it introduced abelian categories and gave us sheaf cohomology as a certain type of derived functor. However, I've heard from various sources (Manin's Homological Algebra, my prof, and the 2 part AMS Notices articles) that one of the famous aspects of this paper is that it "reinterpreted" the basics of combinatorial topology. Does anybody know what this means? Slightly more specific: how was combinatorial topology understood at that time and how did the Tohoku paper force a reinterpretation of the conventional concepts? I know this question might be a bit ill posed, but I'd like to know if somebody understands what this means and can explain it at a first year graduate student level.

Thanks, Ben

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bhwang
bhwang
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Ben
Ben
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Grothendieck's Tohoku Paper and Combinatorial Topology

Hi,

I've read some discussions of Grothendieck's famous Tohoku Paper, and I understand that one reason it was a landmark paper was that it introduced abelian categories and gave us sheaf cohomology as a certain type of derived functor. However, I've heard from various sources (Manin's Homological Algebra, my prof, and the 2 part AMS Notices articles) that one of the famous aspects of this paper is that it "reinterpreted" the basics of combinatorial topology. Does anybody know what this means? Slightly more specific: how was combinatorial topology understood at that time and how did the Tohoku paper force a reinterpretation of the conventional concepts? I know this question might be a bit ill posed, but I'd like to know if somebody understands what this means and can explain it at a first year graduate student level.

Thanks, Ben