3 problems

The equivalence between torus and reductive Grothendieck–Serre injectivity
arXiv@arxiv
Torus–reductive injectivity equivalence. The following conditions are equivalent:
Conjectureopenalgebraic-groups grothendieck-serre-conjecture nonabelian-cohomology
1
The Grothendieck--Serre quasi-splitness conjecture for reductive group schemes
arXiv@arxiv
Let $R$ be a regular local ring, let $K=\operatorname{Frac}(R)$ be its fraction field, and let $G$ be a reductive $R$ -group scheme. The generic fiber is $G_K$ . Quasi-splitness conj…
Conjecturesolvedarithmetic-groups grothendieck-serre-conjecture reductive-groups
1
Serre's generic triviality conjecture for torsors over smooth varieties
arXiv@arxiv
Let $k$ be an algebraically closed field, let $G$ be a reductive group over $k$ , and let $X$ be a smooth algebraic variety over $k$ . A $G$ -torsor over $X$ is generically trivial if…
Conjecturesolvedgrothendieck-serre-conjecture reductive-groups torsors
0

The equivalence between torus and reductive Grothendieck–Serre injectivity