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Feb
1
comment Definition of ind-schemes
Dear @Martin, I appreciate you asking this question! It's something I've wondered about many times before. +1!
Sep
11
awarded  Nice Question
Sep
10
comment Smooth admissible representations, Hom, tensor and extension of scalars
I should say the above holds for an arbitrary group with $V$ and $W$ arbitrary $F[G]$-modules. I don't know what more is true if one supposes $G$ is locally profinite and the representations are (admissible) smooth.
Sep
10
comment Smooth admissible representations, Hom, tensor and extension of scalars
If $V$ is a finitely generated representation, then the map is an isomorphism for any field extension. If $E/F$ is finite, it's an isomorphism for all $V$ and $W$. The map is always injective. This is all independent of the characteristic of $F$.
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