6 votes
Accepted

A complex version of the Cahiers topos

This has already been done, see the article EFC-algebra and references therein. In particular, the paper of Pridham constructs the topos of ∞-sheaves on the site of (derived) Stein spaces and explores ...
Dmitri Pavlov's user avatar
6 votes
Accepted

Criteria for when Gauss-Manin sheaves are vector bundles

If I am reading the assumptions correctly, this should follow from Theorem 6.4 in the paper Luc Illusie, Kazuya Kato and Chikara Nakayama Quasi-unipotent Logarithmic Riemann-Hilbert Correspondences J. ...
Piotr Achinger's user avatar
5 votes

Number of regions created by r hyper-planes in n-dimensional space

One proof is in my book Enumerative Combinatorics, vol. 1, second ed., Proposition 3.11.8. The first proof is due to L. Schläfli, written in 1850-52 but not published until 1901 in Neue allgemeinen ...
Richard Stanley's user avatar
4 votes

Proving that $H^1(X,\mathcal{Hom}(\mathcal{G},\mathcal{E})) \cong \text{Ext}^1(\mathcal{G},\mathcal{E})$ holds for locally free sheaves

This isomorphism holds for any degree of cohomology and it only requires that the first sheaf $\mathcal{G}$ is locally free. This relies on the fact that $\mathcal{H}om(\mathcal{G},-)$ is exact. There ...
Ben C's user avatar
  • 3,281
4 votes
Accepted

Gluing local holomorphic connections

(Updated, as I realized the formula stated by Huybrechts indeed also does make sense without making any identifications.) One should interpret the two sides in the compatibility condition of ...
Richard Lärkäng's user avatar
2 votes
Accepted

Nearby cycles for stacks

I don't know a reference, but let me discuss a strategy for a proof of the comparison that I think should work. By Artin's comparison, if we take a constant sheaf $\mathbb Z/\ell^n$ and then pull back ...
Will Sawin's user avatar
  • 135k
2 votes

Nearby cycles for stacks

I am not sure about the relation between the algebraic nearby cycles functors (at this point, I believe that the algebraic in your mind is the one in étale cohomology, which is somehow analogous but ...
Alexey Do's user avatar
  • 646
1 vote

Request for non-Einstein positive constant scalar curvature Kähler surfaces

I unfortunately am not able to comment, so I’ll have to write what I can say here: As you point out, the compact surfaces admitting Kähler metrics of positive Ricci curvature, i.e., Del Pezzo surfaces,...
KyleBroder's user avatar

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