7 papers · 1 filter
Resolving G-torsors by abelian base extensions
V. Chernousov, Ph. Gille, Z. Reichstein
Let G be a linear algebraic group defined over a field k. We prove that, under mild assumptions on k and G, there exists a finite k-subgroup S of G such that the natural map H^1(K,…
A birational invariant for algebraic group actions
Zinovy Reichstein, Boris Youssin
We construct a birational invariant for certain algebraic group actions. We use this invariant to classify linear representations of finite abelian groups up to birational equivale…
Equivariant Resolution of Points of Indeterminacy
Zinovy Reichstein, Boris Youssin
We prove an equivariant version of Hironaka's theorem on elimination of points of indeterminacy. Our arguments rely on canonical resolution of singularities.
On a property of special groups
Zinovy Reichstein, Boris Youssin
Let G be an algebraic group defined over an algebraically closed field k of characteristic zero. We give a simple proof of the following result: if H^1(L, G) = {1} for some finitel…
Parusiński's "Key Lemma" via algebraic geometry
Zinovy Reichstein, Boris Youssin
The following ``Key Lemma'' plays an important role in Parusinski's work on the existence of Lipschitz stratifications in the class of semianalytic sets: For any positive integer n…
Splitting fields of G-varieties
Zinovy Reichstein, Boris Youssin
Let be an algebraic group, a generically free -variety, and . A field extension of is called a splitting field of if the image of the class of …