bio  website  math.berkeley.edu/~achinger 

location  Berkeley  
age  28  
visits  member for  4 years, 7 months 
seen  55 mins ago  
stats  profile views  2,670 
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

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Ginvariant 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 nonunique, 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

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Ginvariant vector bundle over schemes?
I think the claim about $A^n$ is false: vector bundles on $P^{n1}$ 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 $P^{n1}$ is a counterexample. 
Sep 24 
comment 
Is there a Dmodule theory in characteristic p>0
There are "arithmetic Dmodules" 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 nonhomomorphism? 
Sep 23 
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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 
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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 nonproper 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 
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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 
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padic 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? 