Involutions of varieties and Rost's degree formula

Abstract

To an algebraic variety equipped with an involution, we associate a cycle class in the modulo two Chow group of its fixed locus. This association is functorial with respect to proper morphisms having a degree and preserving the involutions. Specialising to the exchange involution of the square of a complete variety, we obtain Rost's degree formula in arbitrary characteristic (this formula was proved by Rost/Merkurjev in characteristic not two).

Final version. The section on birational invariance of the Segre class has been removed, and will be incorporated into another paper

References in corpus (4)

• Algebraic cobordism
• The index of an algebraic variety
• Norm varieties and algebraic cobordism
• Detection by regular schemes in degree two

Cited by in corpus (3)

• Involutions and Chern numbers of varieties
• Diagonalisable p-groups cannot fix exactly one point on projective varieties
• Motivic Steenrod operations in characteristic $p$