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bio website math.berkeley.edu/~achinger
location Berkeley
age 29
visits member for 5 years, 6 months
seen yesterday
PhD student, UC Berkeley

Jul
30
comment Neighborhoods of a point in fppf topology
No, because finitely presented flat morphisms are open. For example, if we consider the origin inside the union of the two coordinate axes in $\mathbb{A}^2$, every Zariski neighborhood is reducible, and so is every fppf neighborhood.
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
I agree. I think I've seen "good group in the sense of Serre" somewhere before.
Jul
26
revised Relationship between étale and topological $K(\pi,1)$s
added 54 characters in body
Jul
26
answered Relationship between étale and topological $K(\pi,1)$s
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
I think you need to use the orbifold fundamental group of the moduli space (fundamental group of the stack), correct?
Jun
3
awarded  Pundit
Jun
3
comment The unpublished papers in reference to the published papers
I'm against this question being closed. To quote the Help Center, MO questions should be "the sorts of questions you come across when you're writing or reading articles or graduate level books" and "well-defined," which perfectly applies here.
May
1
comment Action of automorphisms on cohomology with supports
Another comment: If $f:X\to X$ is an isomorphism, then $H^n_x(X, f^*(-))$ form a universal $\delta$-functor. The system of maps $f^* : H^n_x(X, -)\to H^n_x(X, f^*(-))$ forms a map between two universal $\delta$-functors, so it suffices to check whether $f^*:H^0_x(X, -)\to H^0_x(X, f^*(-))$ is an isomorphism.
Apr
30
comment Action of automorphisms on cohomology with supports
(An $f:X\to X$ induces maps $H^n_x(X, M)\to H^n_x(X, f^* M)$ and $H^n(X, f_* M)\to H^n(X, M)$ but there is no canonical way of identifying $f^* M$ and $f_* M$ with $M$...)
Apr
30
comment Action of automorphisms on cohomology with supports
How do automorphisms of $X$ act on $H^n_x(X, M)$?
Apr
27
comment Singularities of the moduli stack of polarized hyperkahler varieties
@abx that's right, but $H^2(X, \mathcal{O}_X)$ is nonzero for $X$ hyperkaehler, and we want to study deformations of a pair $(X, L)$.
Apr
27
answered Singularities of the moduli stack of polarized hyperkahler varieties
Apr
27
revised Counterexamples to Elkik's theorem in the non-Noetherian case
corrected spelling of "Ramero"
Apr
23
comment A question about Weil restriction
In definition (1), $\pi_* \mathbb{G}$ is to be considered as a sheaf on the big Zariski (or etale, or ...) site of $C$, associating to a $C$-scheme $D$ the set ${\rm Hom}_{\tilde C}(D\times_C {\tilde C}, \mathcal{G})$, and then the definitions are equivalent. If we consider the small Zariski site of $C$, then of course the two definitions are not equivalent (often $\mathcal{G}$ will have no sections over Zariski opens).
Apr
23
answered Reflexive sheaves on stable curves
Apr
22
comment Deformation of vector bundle on projective space with same Hilbert polynomial as multiple of structure sheaf
This is probably not a very useful observation: if $E$ is stable, then a deformation of $E$ should be stable as well, hence cannot be trivial. Maybe for some obvious reasons I don't see, a v.b. with Hilbert polynomial the same as the trivial bundle cannot be stable...
Apr
11
reviewed Approve Intuition for Integral Transforms
Apr
11
comment Interpreting Frobenius pullback as an invariant differential in the case of an elliptic curve
Is $S$ affine? / Shouldn't $H^1(E, \mathcal{O}_E)$ be $R^1 f_* \mathcal{O}_E$? If $E=S$, we should have ${\rm Lie}(E/S)=0$...
Mar
26
awarded  Self-Learner
Mar
21
comment Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian?
Brilliant! Thank you.