Timeline for Are differential forms related to Azumaya algebras?
Current License: CC BY-SA 4.0
9 events
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| Apr 5, 2020 at 5:55 | review | Close votes | |||
| Apr 5, 2020 at 22:07 | |||||
| Apr 5, 2020 at 5:19 | history | edited | YCor | CC BY-SA 4.0 |
changed tag, removed capitals
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| Aug 18, 2017 at 14:10 | comment | added | abx | About your edited question: for which algebra structure??? | |
| Aug 18, 2017 at 14:04 | history | edited | cheyne | CC BY-SA 3.0 |
added 76 characters in body
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| Aug 16, 2017 at 21:36 | comment | added | Jason Starr | That theorem is due to Kato, and it is discussed in Serre's "Galois cohomology". Serre discusses the difference between fields that are of "cohomological dimension $\leq 1$" and fields that are of "dimension $\leq 1$". The second notion is a strengthening of the first notion intended to incorporate the $p$-torsion of the Brauer group. I believe Gille is writing a book about the corresponding modification of 'etale cohomology (for which "cohomological dimension $\leq 1$" is Serre's notion of "dimension $\leq 1$"). | |
| Aug 15, 2017 at 18:24 | comment | added | Daniel Litt | You may enjoy Theorem 9.2.4 in "Central Simple Algebras and Galois Cohomology" by Philippe Gille, Tamás Szamuely, which classifies $p$-Torsion Brauer classes (in characteristic $p$!) in terms of differential forms. IIRC this theorem is originally due to Kato. I don't know a related result in characteristic zero, which is what you seem to be looking for. | |
| Aug 15, 2017 at 14:02 | comment | added | Fang Hung-chien | Side remark. In characteristic $p$>0, the pushforward of the sheaf of (crystalline) differential operators on $X$ to its Frobenius twist $X^{(p)}$, has a natural Azumaya algebra structure over the structure sheaf of the cotangent bundle of $X^{(p)}$. | |
| Aug 15, 2017 at 13:53 | answer | added | Ben Webster♦ | timeline score: 3 | |
| Aug 15, 2017 at 12:30 | history | asked | cheyne | CC BY-SA 3.0 |