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Apr
26
comment Reference for algebraic manipulation of sheaves
and the first one does not make much sense either ...
Apr
25
reviewed Approve Find a estimate for quasilinear parabolic equation
Apr
12
revised Reference for Manin's idea on algebraic geometry over the symmetric monoidal model category of Motives
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Apr
12
revised Reference for Manin's idea on algebraic geometry over the symmetric monoidal model category of Motives
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Apr
12
answered Reference for Manin's idea on algebraic geometry over the symmetric monoidal model category of Motives
Apr
7
reviewed Approve How do you mentor undergraduate research?
Apr
5
answered Do equivariant morphisms induce representable maps of quotient stacks?
Apr
4
comment Equivariant Riemann-Roch on DM stacks?
But generally I agree with Jason that the question needs to be reformulated more precisely. Do you start with a Deligne-Mumford stack with a group action, or is the equivariant part encoded in the fact that you consider a quotient DM stack ?
Apr
4
comment Equivariant Riemann-Roch on DM stacks?
@Jason Starr : the point of Toen's construction is precisely to use a cohomology theory such that the cohomology of the stack does not coincide rationally with the cohomology of its moduli space (Toen uses, morally, "ordinary" cohomology of the inertia stack). For instance, the cohomology ring of $BG$ is (morally at least) the rational character ring of $G$, and not $\mathbb Q$.
Mar
27
comment Descent of line bundles to the quotient
@abx what you claim is fine for tame actions but may fail in positive characteristic. See the fantastic post of David Rydh : mathoverflow.net/questions/204701/…
Mar
12
awarded  Nice Answer
Mar
8
answered What are parabolic bundles good for?
Feb
17
awarded  Excavator
Feb
17
revised reference for Levelt-Turritin
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Feb
9
comment Degree formalism for line bundles on Deligne-Mumford stacks
A quick way to define the degree is : let $\pi:\mathcal C \to C$ be the morphism to the moduli space. Then $\pi^*: \operatorname{Pic}(C)_{\mathbb Q} \to \operatorname{Pic}(\mathcal C)_{\mathbb Q}$ induces an isomorphism of rational Picard groups, with inverse $\pi_*$. So $\deg\pi_*(\mathcal L)$ is a well defined rational number. This works more generally for Chern classes of vector bundles.
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