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Results tagged with infinity-categories
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user 6074
Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.
13
votes
Can we use Mann's six-functor formalism with D-modules?
I have finally found some time to write up the $6$-functor formalisms in coherent cohomology (a la Gaitsgory--Rozenblyum) and for $D$-modules, see Lecture 8 and its appendix.
A short synopsis is that …
- 21.3k
4
votes
Accepted
Compactly supported sections of coherent sheaves and the dualizing complex
Isn't the dualizing complex defined in general in the proper case by taking applying the right adjoint of $\pi_\ast$ to $k$? That's what I'll take as the definition anyways. The Gorenstein property ju …
- 21.3k
6
votes
Accepted
Derived category of abelian sheaves on a site equivalent to sheaves on the derived category ...
It's true in any $1$-topos for hypercomplete sheaves, see Theorem 2.1.2.2 in Spectral Algebraic Geometry.
- 21.3k
12
votes
Accepted
Cohesion relative to a pyknotic/condensed base
Let me try to cut through the jargon. One thing that confuses me are two uses of "tangent spaces" here, that I believe are quite unrelated. One is the usual notion of tangent spaces of smooth manifold …
- 21.3k
12
votes
Infinity-categorical analogue of compact Hausdorff
That's a good question! I think Barwick and Haine have thought much more about this, and maybe they already know the answer? What I say below is definitely known to them. Also beware that I've written …
- 21.3k
29
votes
Accepted
Condensed criterion for sheafiness of adic spaces
Thanks for the question! One interpretation of the conjecture is true. Let me elaborate. The following results are kind of implicit in some discussion towards the end of www.math.uni-bonn.de/people/sc …
- 21.3k