bio  website  

location  Bloomington, IN  
age  28  
visits  member for  5 years, 4 months 
seen  12 hours ago  
stats  profile views  2,147 
I am a postdoc at Indiana University. I got my Ph.D. in May 2014 from UT Austin.
1d

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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. 
1d

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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 nonzero 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 
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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 LFspace (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 padic representation of the absolute Galois group of Q_p
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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 
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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). 
May 14 
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Extension of scalars and projective limits
Dear @Fred Rohrer, A ring map of finite presentation is one which makes the target into a finitely presented algebra over the source (this is common usage in commutative ring theory). It would be clearer probably to say that $h$ makes the target into a finitely presented module over the source. 
May 11 
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Weil group of a local field, small notational problem
The choice of $\Phi$ is equivalent to the choice of a splitting, since $\Omega_F$ is profinite and $\widehat{\mathbf{Z}}$ is the ``free profinite group on one element." In my answer I'm making the resulting splitting homomorphism (semi)explicit. 
May 11 
answered  Weil group of a local field, small notational problem 
Apr 26 
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All nonsplit Cartan subroups of $GL_2(\mathbb{Z}/n\mathbb{Z})$ are conjugate
Dear @grghxy, By unmarried, you mean unramified? :) 