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Jan
11
awarded  Custodian
Jan
11
reviewed Approve Groups with probability measures
Jan
1
comment What is the first cohomology $H_{fppf}^{1}(X, \alpha_{p})$?
And since $\operatorname{Pic}_{X/k}[p]\simeq \left( \mathbb Z /p \right)^h \times \left(\mu_p\right)^h \times \left(\alpha_p\right)^{2(g-h)}$, where $h$ is the $p$-rank, if I am correct, we are almost done.
Dec
28
comment Extension of sheaf of Azumaya algebras and derived equivalence
"I wish $(X', \mathcal{A})$ to be reasonably closed to $(X', \mathcal{A})$". This shouldn't be too hard.
Dec
24
answered Quotient of a smooth curve by a finite group and differentials
Dec
19
awarded  Yearling
Nov
20
comment Definition of étale (etc) for non-representable morphisms of algebraic stacks?
@Qfwfq your root stack is a gerbe, banded by $\mathbf \mu_r$. For gerbes there seem to be specific conventions (the influence of Tannaka theory ?) for instance the gerbe has P if the band has. In this case you probably have to assume that $r$ is invertible.
Nov
20
comment Definition of étale (etc) for non-representable morphisms of algebraic stacks?
@Ariyan Javanpeykar : for finite morphisms, I doubt it. For instance they are defined as quasi-finite and proper in the reference text : Vistoli, Angelo Intersection theory on algebraic stacks and on their moduli spaces.ams.org/mathscinet-getitem?mr=1005008 definition 1.8
Nov
19
answered How do we get the quotient $Ext^1(N,M)/Hom(N,M)$?
Jul
25
comment Relationship between étale and topological $K(\pi,1)$s
Question 2 is reminiscent of the Malcev-Grothendieck theorem : if the étale fundamental group of a smooth complex projective variety is trivial, then there is no non-trivial bundle with a flat connection. See the introduction of arxiv.org/abs/1112.4603 .
Jul
13
answered Is there a “free abelian group of rank 1” in the category of affine group schemes?
Jun
6
comment Kähler differentials, intuition behind $\text{div}(\omega)$, canonical divisor on algebraic curves?
Well reading Hartshorne's chapter on curves should be more than enough. You will learn more doing this job by yourself than taking the easy option of asking the question here, where it is not really appropriate.
Jun
6
comment Intuition for thinking about $R$-module of Kähler differentials, universal receptacles, derivations?
not a research level question in my opinion.
Jun
6
comment Kähler differentials, intuition behind $\text{div}(\omega)$, canonical divisor on algebraic curves?
not a research-level question in my opinion.
May
27
comment lifting morphism of torsors
Don't you mean $H^1(X,\mathfrak{g}_P\otimes I)$ instead of $H^1(X,\mathfrak{g}_P)$ ?
May
25
comment Do line bundles descend to coarse moduli spaces of Artin stacks with finite inertia?
@David Rydh: thanks for the explanation.
May
25
comment Differentials for algebraic stacks
The twist in $\mathfrak{g}^\vee[1]$ seems wrong to me, I think $\mathfrak{g}^\vee[-1]$ is correct.
May
12
comment Do line bundles descend to coarse moduli spaces of Artin stacks with finite inertia?
Thanks for the answer ! In proof of Lemma 2 : "Since $Z\to X$ is finite, we can trivialize $\mathcal{L}$ étale-locally on $X$". I don't get it - could you elaborate ? Sorry if I am missing something obvious.
May
5
comment Do line bundles descend to coarse moduli spaces of Artin stacks with finite inertia?
@Zsolt Patakfalvi : you are right that Alper's criterion is "the stabilizers act trivially on the fibers" and not stalks. And I was indeed assuming that the moduli space is good.
May
5
comment Do line bundles descend to coarse moduli spaces of Artin stacks with finite inertia?
You can probably answer positively (for S quasi compact) by using Alper's criterion : namely a vector bundle descends to the moduli space iff the stabilizers act trivially on the stalks. See his paper "Good moduli spaces for Artin stacks" Theorem 10.3 .