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Results tagged with grothendieck-topology
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user 2191
17
votes
Accepted
Voevodsky's Triangulated Categories of Motives and their Relationships
I'm not sure that it is possible to compress the big picture into one answer; yet I will try to give a hint.
Firstly, one can hardly hope to have a "reasonable" motivic $t$-structure for motives with …
- 16.9k
4
votes
0
answers
259
views
Can one construct Freyd-Mitchell's embeddings that respect sheafifications?
For a certain presheaf $P$ with values in an abelian category $A$ satisfying AB5 and its sheafification $S$ (with respect to a small Grothendieck site) I would like to prove: $S(f):S(X)\to S(Y)$ is a …
- 16.9k
3
votes
Grothendieck topologies, Mayer-Vietoris, and points
You definition of a cohomology theory is rather strange since it does not seem to depend on the choice of the site (it corresponds to Zariski topology).
For the correct definition of cohomology theo …
- 16.9k
2
votes
0
answers
354
views
What are the easiest cases of base change (for sheaves on sites)?
I have a closed embedding of schemes $i:X'\to X$, and for each of them I consider three Grothendieck topologies for the category of the corresponding (relatively) \'etale schemes: the \'etale one, the …
- 16.9k