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4 votes
0 answers
87 views

Levis, parabolics and Bruhat-Tits over Henselian local rings

Let $(R,m)$ be a Henselian local ring with algebraically closed or finite residue field $k$ and fraction field $F$. For example, we may work with $R=W(\mathbb F_p^{alg})$. The paper "Reductive ...
Zhiyu's user avatar
  • 6,622
7 votes
1 answer
310 views

Faithful representations of integral models

I am reposting a question that I had asked on stackexachage three weeks ago. Let $G/\mathbb{Q}$ be a connected reductive group, and $\mathcal{G}/\mathbb{Z}$ be an integral model (i.e. flat affine ...
Coherent Sheaf's user avatar
2 votes
0 answers
258 views

Is a reductive group scheme always parahoric?

Let $R$ be complete (or, more generally, Henselian) discrete valuation ring with fraction field $K$. Let $G$ be a reductive $R$-group scheme. Is $G$ a parahoric in the sense of Bruhat-Tits? If so, ...
Question Machine's user avatar
2 votes
2 answers
266 views

Openness of finite index subgroups of $\mathrm{GL}_n(\prod O_v)$

Let $K$ be a global field and set $O := \prod_{v\nmid \infty} O_v$ where $v$ runs over the finite places of $K$. Equip $\mathrm{GL}_n(O) = \prod_v \mathrm{GL}_n(O_v)$ with the product of the $v$-adic ...
Question Mark's user avatar
45 votes
2 answers
3k views

What are the possible motivic Galois groups over $\mathbb Q$?

Let $E$ be a motive over $\mathbb Q$. (I should precise, that by a motive I mean here a pure motive over $\mathbb Q$, with coefficients in $\mathbb Q$, that I see here as a conjectural object which ...
Joël's user avatar
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