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 and Merkurjev in characteristic not two).
Haution, O. (2018). Involutions of varieties and Rost's degree formula. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 2018(745), 231-252 [10.1515/crelle-2016-0003].
Involutions of varieties and Rost's degree formula
Haution O.
2018
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 and Merkurjev in characteristic not two).
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