4,425 reputation
1532
bio website math.berkeley.edu/~achinger
location Berkeley
age 28
visits member for 5 years, 1 month
seen 20 hours ago
PhD student, UC Berkeley

1d
awarded  Self-Learner
Mar
21
comment Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian?
Brilliant! Thank you.
Mar
21
accepted Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian?
Mar
17
revised Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian?
added 5 characters in body; edited title
Mar
17
asked Is the ring $\mathbb{Z}_p [[x]]\otimes_{\mathbb{Z}_p} \overline{\mathbb{Q}}_p$ Noetherian?
Mar
13
comment Covering of schemes and flatness
The normalization of a cuspidal curve is a bijective finite map which is not flat.
Feb
19
comment Artin approximation of a diagram
What do you mean by approximate? Whether there exists a $\phi'$ in some etale neighborhoods inducing $\phi$ upon completion? Then the answer is no as we can take $Z$ to be a point, $(X, x)=(\mathbb{A}^1, 0)$, $(Y, y) = (\mathbb{A}^1, 1)$ and $\phi = \exp$. Or approximate up to order $N$ for any given $N$? Then I think the answer is yes, because we can apply approximation to the graph of $\phi$.
Feb
9
comment Definition and sigularity of Ramified covers
In general the cyclic cover will be ramified everywhere on $D$, so if $D\cap {\rm Sing}(X)$ is big there is no hope.
Feb
9
comment Definition and sigularity of Ramified covers
Be careful, because the cyclic covers as defined need not be normal if $D$ is non-reduced: in the simple example $X=\mathbb{A}^1$, $D=2\cdot (x)$ the recipe gives the non-normal $\tilde X = {\rm Spec}(k[x,y]/(x^2-y^3)$. But it's easy to compute the normalization, which is ${\rm Spec_X} \bigoplus_{i=0}^{n-1} \mathcal{O}_X(\lfloor \frac{i}{n}D \rfloor)$.
Feb
6
awarded  Yearling
Feb
2
awarded  Popular Question
Feb
1
comment Reference request: log Fano varieties
What if $X$ is not projective?
Jan
29
awarded  Popular Question
Jan
13
comment Intersections of $B$ and $B^-$ orbits in the flag variety $G/B$
It is also stated there that their closures are Cohen-Macaulay, so in particular they are equi-dimensional.
Jan
13
comment Intersections of $B$ and $B^-$ orbits in the flag variety $G/B$
I think they are called (open) Richardson varieties. Their dimensions are described here: arxiv.org/pdf/1008.3939v2.pdf (page 2).
Jan
12
awarded  Guru
Jan
8
comment Is there a “simplification” functor in algebraic topology?
Universal in the homotopy category, I presume?
Jan
8
awarded  Taxonomist
Dec
28
comment Coherent sheaves on Proj
Note that q.c. sheaves on $Proj(S)$ are the same as $\mathbb{G}_m$-linearized sheaves on $Spec(S)\setminus \{m\}$ where $m = \bigoplus_{n>0} S_n$ is the irrelevant ideal. So you are asking for a criterion for an $S$-module $M$ being zero away from $m$. But this is equivalent to asking when $M_x = 0$ for each $x\in m$. So the criterion (for a f.g. module) is: iff $m^k M = 0$ for some $k>0$. This in turn is clearly equivalent to $M$ having only finitely many nonzero degrees.
Dec
24
comment Blow-ups of $\mathbb{P}^{n-3}$ and $(\mathbb{P}^1)^{n-3}$
It is indeed toric - it's the identity on the torus, and the analysis of fans is used to show that it extends to the open orbits of the boundary divisors.