Timeline for Should all cohomology theories have a smooth proper base change
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2016 at 19:05 | comment | added | Mikhail Bondarko | For h-topology you will just get the corresponding etale cohomology.:) For other topologies one has to compute... | |
| Dec 8, 2016 at 18:44 | comment | added | Ciro | @MikhailBondarko Thank you for your comment. I see now that I was being too vague in my question (and comment). My apologies. Let me ask a slightly more precise question: Does smooth proper base change with finite abelian coefficients fail "for obvious reasons" for other cohomology theories like Nisnevich, h-topology, fppf, etc? | |
| Dec 8, 2016 at 18:37 | comment | added | Mikhail Bondarko | Proper base change is only true for etale cohomology with (locally?) CONSTANT coefficients. This is a very specific property! | |
| Dec 8, 2016 at 18:34 | comment | added | Ciro | @MikhailBondarko The cohomology theories I am familiar with (eg etale cohomology) satisfy smooth proper base change if one avoids certain characteristics. Does smooth proper base change fail for Nisnevich or some other Grothendieck topology? | |
| Nov 30, 2016 at 21:57 | comment | added | Mikhail Bondarko | The answer is definitely "no" for the first part of your question, and it is rather difficult to formulate a conjecture on motives that would be related to its second part. | |
| Nov 30, 2016 at 21:49 | history | asked | Ciro | CC BY-SA 3.0 |