2,212 reputation
1825
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location Bloomington, IN
age 28
visits member for 5 years, 6 months
seen 3 hours ago

I am a postdoc at Indiana University. I got my Ph.D. in May 2014 from UT Austin.


Aug
4
revised Three and a half basic questions on the Weil restriction of scalars
changed instance of "ring" to "field"
Jul
30
comment Absolutely irreducible p-adic representation of the absolute Galois group of Q_p
Dear Joël, this might be a silly question, but do elliptic curves over $\mathbf{Q}$ easily provide examples where Chenevier's theorem gives an open image representation? There are no elliptic curves with conductor equal to any of those primes, and for $p\geq 11$, there are examples where the representation doesn't have the same image as its restriction to a decomposition group at $p$.
Jul
12
comment Zariski closure construction (over a field) implicitly uses reduced induced structure?
Thank you @grghxy.
Jul
11
asked Zariski closure construction (over a field) implicitly uses reduced induced structure?
Jul
4
comment How Does a Borel Subgroup Know Which Weights Are Dominant
first act on the character being $\lambda$ by the longest Weyl group element to get something which is actually $\overline{B}$-dominant.
Jul
4
comment How Does a Borel Subgroup Know Which Weights Are Dominant
Dear @David, I don't have my copy of Jantzen with me, but I think if you work in the algebraic category (algebraic induction, etc.), things are as follows. If you take a $B$-dominant weight and induce it from the opposite Borel $\overline{B}$ (relative to $B$) then what you get is a non-zero representation whose socle (in characteristic zero, just the whole thing due to semisimplicity) is the representation of your group $G$ with highest $B$-weight $\lambda$. If you induce from $\overline{B}$ a weight which is not $B$-dominant, then you get zero. If you want to induce from $B$, you should
Jun
30
revised Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
edited body
Jun
30
accepted Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
Jun
30
answered Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
Jun
29
comment Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
Okay, I expected the basic version was adequate. I think I understand. Thank you.
Jun
28
comment Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
Dear @grghxy, Perhaps I'm missing the point, and this is overkill, but the most general version of the open mapping theorem I know of has the source an LF-space (locally convex inductive limit of a sequence of Fréchet spaces), but I don't see why $\mathscr{O}(U)$ has this structure without further hypotheses. I'm assuming you're suggesting applying the open mapping theorem to the continuous bijection $\mathscr{O}(U)\to E$, where $E$ is the equalizer equipped with its Banach structure and deducing that this map is open.
Jun
28
revised Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
added 179 characters in body
Jun
28
comment Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
Dear @grghxy, Thanks for the response and for pointing out my oversight. I was thinking of affinoid spaces.
Jun
28
revised Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
added 42 characters in body
Jun
28
asked Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
Jun
9
awarded  Excavator
Jun
9
revised Absolutely irreducible p-adic representation of the absolute Galois group of Q_p
added 1 character in body
Jun
6
revised discrete valuation ring and ring of witt vectors
added 1 character in body
Jun
6
answered discrete valuation ring and ring of witt vectors
May
31
comment A galois group is topologically finitely generated or finitely generated as a $\mathbb{Z}_p$-module
I don't have the book at home so I can't give a precise reference, but this fact is essentially proved in Washington's book on cyclotomic fields, in proving a bound on the number of "independent" $\mathbf{Z}_p$-extensions of a number field. The proof is based on the idelic description of global class field theory and the key fact is that the group of principal units in a $p$-adic field is a finitely generated $\mathbf{Z}_p$-module (which is the same thing as a topologically finitely generated abelian pro-$p$ group).