Timeline for Grothendieck categories and their morphisms
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 4, 2020 at 19:11 | comment | added | Ivan Di Liberti | Yes, that's what I mean. | |
| May 4, 2020 at 17:58 | comment | added | Tim Campion | Is a "flat morphism" of Grothendieck categories a functor with an exact left adjoint? | |
| Apr 6, 2020 at 21:15 | comment | added | Leo Alonso | Basically there are two kind of cohomological coefficients continuous and discrete (after Grothendieck). The former are basically quasi-coherent sheaves, the latter local systems in the classical case. As Zariski topology does not capture well the discrete coefficients one has to switch topos and consider the Étale topology and for p-torsion crystalline cohomology. Every theory has an associated Grothendieck category of abelian sheaves (with extra structure). | |
| Apr 6, 2020 at 19:18 | history | edited | Ivan Di Liberti | CC BY-SA 4.0 |
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| Apr 6, 2020 at 19:10 | comment | added | Ivan Di Liberti | @R.vanDobbendeBruyn I like your comment and I am not sure about what I should want, I invite you to elaborate it. I know nothing about etàle site. What story do they tell? | |
| Apr 6, 2020 at 17:49 | comment | added | R. van Dobben de Bruyn | Small comment: there are multiple sources of sheaf categories in algebraic geometry. Flatness is automatic when the structure sheaf is constant (e.g. the étale site with sheaves of $\mathbf Z/n$-modules), but in the quasi-coherent setting is related to the change of rings $f^{-1}\mathcal O_Y \to \mathcal O_X$ (see for example Tag 04JA). Which of the two are you trying to capture? | |
| Apr 6, 2020 at 13:04 | history | asked | Ivan Di Liberti | CC BY-SA 4.0 |