All Questions
Tagged with p-adic-groups ag.algebraic-geometry
13 questions
14
votes
3
answers
2k
views
Naïve definition of parahoric subgroup
Background
Let $F$ be a $p$-adic local field, and let $G$ be a connected reductive group over $F$. Recall that there is a rich theory of compact open subgroups of $G(F)$ which is, essentially, ...
- 843
6
votes
1
answer
394
views
On the Artin-Rees Lemma for non-commutative rings
Consider a commutative noetherian ring $A$ with an ideal $I\subset A$. The Artin-Rees lemma implies that for f.g. modules $N\subset M$, the $I$-adic topology on $N$ agrees with the subspace topology ...
- 541
4
votes
1
answer
1k
views
Closed subgroups of a $p$-adic algebraic group
Let $F$ be a finite extension of $\mathbb{Q}_p$ and $G$ the group of rational points of an algebraic group defined over $F$, endowed with the natural topology. Any Zariski closed subgroup $H \subset G$...
- 3,605
4
votes
0
answers
177
views
Reference for Iwahori-Hecke algebras
I recently came across the notion of an Iwahori-Hecke algebra. I would like to learn the basics about this type of algebras (mainly to get an intuition about them, as they seem to be related to some ...
- 541
3
votes
2
answers
752
views
orbits of linear algebraic group $G({\Bbb Q}_p)$ acting on subgroups of ${\Bbb Q}_p^n$
Let $G\subseteq GL(n)$ be a linear algebraic group, and let $G({\Bbb Q}_p)\subseteq GL(V)$ act on a ${\Bbb Q}_p$-vector space V of finite dimension.
Consider the action of $G$ on abelian subgroups $L\...
- 1,299
3
votes
1
answer
335
views
Abelian varieties as analytic manifolds
Assume we have an Abelian varieties over the p-adic numbers, namely $
k=\mathbb{Q}_p$. Then the question is whether $A(k)$, the rational points over $k$, will form a p-adic analytic manifold.
I am ...
- 315
3
votes
1
answer
643
views
Abelian varieties over $p$-adic fields
Theorem : Let $A$ be an abelian varieties of dimension $d$ over a field $k$, non-archimedian valued complete, i.e. $\mathbb{Q}_p$, then $A(k)$ contains a subgroup of finite index analytically ...
- 315
3
votes
0
answers
138
views
density of unipotent flows in algebraic groups
Let $\mathcal{G}$ be a reductive algebraic group over $\mathbb{Q}$ with a model $G$ over $\mathbb{Z}$ such that $G(\mathbb{R})$ is compact modulo centre. Let $T$ be a maximal torus of $\mathcal{G}$. ...
- 81
3
votes
0
answers
237
views
What's the unipotent radical of the reduction of a bad orthogonal group?
Consider a DVR $A$ with fraction field $K$ and residue field $k$. Assume $2 \in A^\times$. Let $Q: A^n \rightarrow A$ be a quadratic form defined over $A$. Then one has the (naively defined) ...
- 13.3k
2
votes
0
answers
118
views
Growth of invariants in mod-$p$ representations of $\mathrm{GL}_n$
Let $G$ be smooth admissible mod-$p$ representations of $\mathrm{GL}_n(\mathbb{Q}_p)$. Also suppose $\pi$ is an irreducible infinite-dimensional smooth admissible representation of $G$ over $\mathbb{F}...
2
votes
0
answers
118
views
Symmetric spaces which are compact modulo the unipotent radical are compact
Is the following true?
Let $X = G/H$ be a symmetric space of a reductive group over a p-adic field $F$.
Let $X^0$ be an open orbit w.r.t. the action of the minimal parabolic $B$ of $G$.
Let $U$ be ...
- 2,639
1
vote
0
answers
247
views
J. Tate's article on $p$-divisible groups
I have a question about a conclusion that J. Tate arrived at in his paper $p$-Divisible Groups (in: Springer T.A. (eds) Proceedings of a Conference on Local Fields. Springer, Berlin, Heidelberg (1967) ...
- 5,998
1
vote
0
answers
230
views
Group schemes and Hyperspecial maximal compact subgroups
Let $F$ be a number field. For each non-archimedean place $v$ let $O_v$ denote the ring of integers. Let $G$ be a connected linear algebraic group defined over $F$. Consider the set of sequences $(K_v)...
- 223