3,619 reputation
1026
bio website math.berkeley.edu/~achinger
location Berkeley
age 27
visits member for 4 years, 5 months
seen 16 hours ago
PhD student, UC Berkeley

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.
May
20
awarded  Nice Answer
May
20
comment Simultaneous resolution of singularities in special cases of flat families of projective varieties
@Sasha Aaah, I thought the question was asking for $\tilde\mathcal{X}$ smooth over $B$... I apologize for bringing confusion.
May
19
comment Simultaneous resolution of singularities in special cases of flat families of projective varieties
@Sasha could you please expand on that comment? Being flat over $B$ roughly means no components in fibers and no embedded points. I believe a relative resolution could work if the loci we blow up are flat over $B$, but I don't see how to guarantee that the new blow-up loci will be flat.