3,689 reputation
1026
bio website math.berkeley.edu/~achinger
location Berkeley
age 28
visits member for 4 years, 6 months
seen 11 mins ago
PhD student, UC Berkeley

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?
May
29
comment Descend of etale morphism
This is the general "spreading out". The claim is that given a finite diagram of finite type schemes over $\bar k$, there exists a finite extension $k'$ of $k$ and a model of the diagram over $k'$. If your diagram consists of just a single affine (or projective) scheme $X$, write $X = Spec(\bar k[x_1, \ldots, x_n]/(f_1, \ldots, f_r))$ (resp. $Proj(...)$), and let $k'$ be the extension of $k$ generated in $\bar k$ by the coefficients of the $f_i$, then we have a model $X_0=Spec(k'[x_1, \ldots, x_n]/(f_1, \ldots, f_r))$ (resp. $Proj(\ldots)$) over $k'$.
May
29
comment Descend of etale morphism
Why do you think this would be true? You can get a model over a finite extension of $k$, but certainly not over $k$. For example, take $X$ to be an elliptic curve with no rational points over $k$, and $f:Y\to \bar X$ a $2$-isogeny.
May
27
comment What implications would a solution of the *Standard Conjectures* have on the *Hodge Conjecture*?
I thought the implication goes the other way: the Hodge conjecture implies some of the standard conjectures.
May
27
awarded  Nice Question
May
23
revised (When) is isomorphism on differentials enough to guarantee that a map is étale?
typesetting
May
23
revised Examples for Kawamata-Viehweg vanishing fails without normal crossing condition
his proof -> Kawamata's proof
May
23
reviewed Approve suggested edit on Functional equation and conductor for a Rankin-Selberg convolution
May
23
revised (When) is isomorphism on differentials enough to guarantee that a map is étale?
X and Y are now flat over S; added an idea for Y smooth/S; added 1 character in body
May
23
revised (When) is isomorphism on differentials enough to guarantee that a map is étale?
now X and Y are flat over S
May
23
revised (When) is isomorphism on differentials enough to guarantee that a map is étale?
added an alternative version of the question (X reduced)
May
23
comment (When) is isomorphism on differentials enough to guarantee that a map is étale?
Related (but doesn't answer the question): mathoverflow.net/questions/41/…
May
23
asked (When) is isomorphism on differentials enough to guarantee that a map is étale?
May
22
comment Correct spelling of names, Chebychev and Cholesky
Why not ask Wikipedia? Cholesky was not a Russian, as far as I know.