Timeline for How is etale cohomology of integer rings related to Galois cohomology?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 23, 2011 at 13:39 | comment | added | Olivier | @Mephisto I have explained myself clumsily. What I meant more precisely was something along these lines. Say you are in the late 80s/early 90s and you are listing the tools you need for the conjectures you have in mind: duality for cohomology over l.c.n rings, some results on perfect complexes, comparison theorems, base-change for some cohomology complexes, excision... None of these results had clear, complete references at the time but there were no point restricting yourself to Galois cohomology (SGA XVII, Mazur 1973 and being Bloch-Kato would in fact rather suggest otherwise). | |
| Apr 23, 2011 at 11:17 | comment | added | mephisto | @Loeffler. The spectral sequence and a proof of its degeneration can be found in Milne's ADT II Proposition 2.9. @Olivier. The results you mention are hardly "classical Well-known results". As far as I know, all such results had correct complete proofs in the literature by the mid-80s or earlier (not late 90s). For example, Poitou-Tate is proved in Haberland 1978. By contrast, the first complete proof in the literature of the very basic Artin-Verdier duality theorem is in ADT (1986), but that contained an error which wasn't fixed until the second edition (2004). | |
| Apr 23, 2011 at 8:30 | comment | added | Olivier | Or think of the excision map in Galois cohomology with restricted ramification. | |
| Apr 23, 2011 at 7:32 | comment | added | Olivier | @Mephisto Central to the approach of Kato is the fact that the étale cohomology of a perfect complex of étale sheaves is a perfect complex. In the early 90s, I wouldn't know what source to quote for the corresponding statement in Galois cohomology. But even something as "basic" as Poitou-Tate had no clear reference before the first edition of Milne's ADT, and that's only from 1986. | |
| Apr 23, 2011 at 7:28 | history | edited | Olivier | CC BY-SA 3.0 |
Answered a question in comments
|
| Apr 23, 2011 at 7:11 | comment | added | David Loeffler | This is probably just me being slow, but could you elaborate a bit more on the spectral sequence argument? (For instance, what is this spectral sequence converging to?) | |
| Apr 23, 2011 at 6:54 | vote | accept | David Loeffler | ||
| Apr 22, 2011 at 21:49 | comment | added | mephisto | "In fact, many classical well-known results were given correct complete proofs only very late (in the late 90s in some cases)." Which results are you thinking of? | |
| Apr 22, 2011 at 19:54 | history | answered | Olivier | CC BY-SA 3.0 |