All Questions

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):...

The following statement seems to be well-known: Let $X$ be a variety on which an affine algebraic group $H$ acts with finitely many orbits and let $s \in H$ be semisimple. Then $H_s = \{h \in H \mid ...

Does there exist a reductive group $G$ of type $E_7$ over a given totally real field $L^+$ such that for every embedding $\tau:L^+\to \mathbb{R}$ except one , $G_{\tau,\mathbb{R}}(\mathbb{R})$ is ...

Generally one considers a vector space $k^n$, then $\mathrm{GL}_n(k)$ is realized as the set of automorphisms of $k^n$. We have $k^m\times k^n = k^{m+n}$, however under the natural embedding, $\mathrm{...

Let $f:X\to Y$ be a surjective morphism between two projective schemes over a field of characteristic $p>0$. Also assume that $X$ is smooth,$Y$ smooth & irreducible and $f_*\mathcal{O}_X=\...

Let $E$ be a supersingular elliptic curve over $\mathbb{F}_p(t)$. Is something known on the $p$-torsion of the Tate–Shafarevich group in this case? In particular, I would like to know if (or if known ...