3,791 reputation
1026
bio website math.berkeley.edu/~achinger
location Berkeley
age 28
visits member for 4 years, 7 months
seen 55 mins ago
PhD student, UC Berkeley

1h
comment analogy between connections and $\ell$-adic sheaves: what happens with the residue?
An extension of the sheaf to the Kummer \'etale site of $(X, D)$ (where we allow covers tamely ramified along $D$)?
1d
comment G-invariant vector bundle over schemes?
"$G$-invariant" per se doesn't make much sense: it would mean $g^* E = E$ for every $g\in G$, but there is a choice involved! This leads to the notion of linearization of a vector bundle $E$: it's an isomorphism $f:\pi^* E \to \mu^* E$, where $\pi, \mu:G\times X\to X$ are the projection resp. the action, satisfying a certain "cocycle condition". The pair $(E, f)$ is called a $G$-equivariant bundle. This $f$ may be non-unique, as the example of $E=\mathcal{O}_X$ on $X=\mathbb{A}^1$ with the usual $\mathbb{G}_m$-action shows (here one has $\mathbb{Z}$ worth of possible choices).
1d
comment G-invariant vector bundle over schemes?
I think the claim about $A^n$ is false: vector bundles on $P^{n-1}$ correspond to $G_m$-equivariant vector bundles on $A^n \setminus \{0 \}$, and these don't have to extend to vector bundles on $A^n$. The tangent bundle of $P^{n-1}$ is a counterexample.
Sep
24
comment Is there a D-module theory in characteristic p>0
There are "arithmetic D-modules" of Berthelot, maybe that's close to what you're looking for?
Sep
23
comment A simple example of a ring that is an $A$-module but not an $A$-algebra?
$A=\mathbb{Z}[x]$, with $x$ acting on $B$ by any additive non-homomorphism?
Sep
23
comment Raikov's thm: Given two rv X,Y with $X+Y=Z\sim Poisson(\lambda)$, then X,Y is Poisson
I remember Oleszkiewicz assigned this as a homework problem but no one solved it ;)
Sep
19
comment Compute higher direct image for Gm under open embedding
To show that some presheaf $F$ sheafifies to zero is the same as showing that given a section $s\in F(V)$, we can cover $V$ by $V'_i$ such that $s$ maps to zero in $F(V'_i)$. In other words, for every $x\in V$ there is a $V'_x$...
Sep
19
answered Compute higher direct image for Gm under open embedding
Sep
17
answered deformations of vector bundles on curves
Sep
14
comment If the direct image of f preserves coherent sheaves on notherian schemes,how to show f is proper?
A good example of such would be the structure sheaf of an incomplete (so affine) closed curve on this non-proper variety. You get such curves thanks to the valuative criterion of properness.
Sep
6
accepted Embedded resolution of curves on smooth varieties
Sep
6
asked Embedded resolution of curves on smooth varieties
Sep
6
reviewed Approve suggested edit on Can we recover a von Neumann algebra from its predual?
Aug
9
comment $X$-points of reductive group schemes, if $X$ is a proper smooth curve over a finite field
I don't understand something. Since $G$ is affine over $X$, assuming it's of finite type, we can embed $G$ into $\mathbb{A}^n\times X$ for some big $n$. This reduces the question to $G = \mathbb{A}^n\times X$, in which case the answer is trivially yes as $\Gamma(X, \mathcal{O}_X)^n$ is a finite group...
Aug
8
comment Finite extension of local fields
I thought that "local field" means a complete discretely valued field with perfect residue field... The above naturally doesn't work in the case of finite residue fields.
Aug
8
answered Finite extension of local fields
Jul
19
comment p-adic etale cohomology
I think the answer is yes thanks to $p$-adic Hodge theory: after tensoring with $B_{cris}$ and taking Galois invariants, we get $H^i_{cris}(X/\mathbb{Z}_p)$ with the Frobenius, which then we can use to count points in the special fiber.
Jul
2
awarded  Curious
Jun
26
awarded  Citizen Patrol
Jun
5
answered Are quotients of affine schemes by finite groups faithfully flat?