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Intersections of two quadrics and Chatelet surfaces. II.

J.-L. Colliot-Thélène, J.-J. Sansuc (1987)

Journal für die reine und angewandte Mathematik

Introduction to actions of algebraic groups

Michel Brion (2010)

Les cours du CIRM

These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.

Invariant theory for linear algebraic groups II (char k arbitrary)

A. Fauntleroy (1988)

Compositio Mathematica

Invariant theory for $S_{5}$ and the rationality of $M_{6}$

N. I. Shepherd-Barron (1989)

Compositio Mathematica

Invariants, torsion indices and oriented cohomology of complete flags

Baptiste Calmès, Viktor Petrov, Kirill Zainoulline (2013)

Annales scientifiques de l'École Normale Supérieure

Let $G$ be a split semisimple linear algebraic group over a field and let $T$ be a split maximal torus of $G$ . Let $𝗁$ be an oriented cohomology (algebraic cobordism, connective $K$ -theory, Chow groups, Grothendieck’s $K_{0}$ , etc.) with formal group law $F$ . We construct a ring from $F$ and the characters of $T$ , that we call a formal group ring, and we define a characteristic ring morphism $c$ from this formal group ring to $𝗁 (G / B)$ where $G / B$ is the variety of Borel subgroups of $G$ . Our main result says that when the torsion index...