Questions tagged [reductive-groups]

In Borovoi's paper Abelian Galois cohomology of reductive groups, the algebraic fundamental group of a connected reductive group $G$ over a field $K$ of characteristic zero is defined as $$\pi_1(G, T):...

Let $F$ be a local field of characteristic $0$, $G=\mathrm{GL}_n(F)$. When $F$ is $p$-adic, Bernstein and Zelevinsky classified the irreducible generic representations. The statement is: Let $\delta_{...

For a semisimple complex Lie algebra $\mathfrak{g}$ and a regular element $X\in \mathfrak g$ the centralizer of $X$ in $\mathfrak g$ is a Cartan subalgebra (see Knapp, 'Lie Groups beyond an ...

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 ...

Let $G$ be a reductive group. If one can associate to $G$ a Shimura datum $(G,X)$, then the étale cohomology of the associated Shimura variety $\operatorname{Sh}(G,X)$ is a strong tool for the ...