bio | website | math.berkeley.edu/~achinger |
---|---|---|
location | Berkeley | |
age | 28 | |
visits | member for | 4 years, 8 months |
seen | 25 mins ago | |
stats | profile views | 2,759 |
PhD student, UC Berkeley
Oct 12 |
awarded | Benefactor |
Oct 12 |
accepted | Can we normalize a complex analytic space in a covering of an open subset? |
Oct 5 |
awarded | Promoter |
Oct 5 |
answered | Soft question: beginners reference to moduli spaces |
Oct 5 |
comment |
G-equivariant coherent sheaves on Bott-Samelson Resolutions
@Sasha yes, Schubert varieties have rational singularities. |
Oct 2 |
asked | Can we normalize a complex analytic space in a covering of an open subset? |
Oct 2 |
answered | Flatness of Normaliztion of regular schemes |
Sep 30 |
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 $D$)? |
Sep 29 |
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). |
Sep 29 |
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 |
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 noetherian 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... |