Zero-cycles on a twisted Cayley plane

TL;DR

This paper proves that for certain algebraic varieties associated with exceptional groups over fields with characteristic not 2 or 3, the degree map on zero cycles is injective, extending previous results to more types.

Contribution

It extends the injectivity result of the degree map on zero cycles to varieties of types F_4, E_6, and E_7 with trivial Tits algebras, including new cases for E_7.

Findings

Injectivity of the degree map on zero cycles for F_4, E_6, E_7 varieties

Extension of previous results to additional exceptional group types

Applicable over fields with characteristic not 2 or 3

Abstract

This is an essentially extended version of the preprint dated by August 2005 (this includes now the varieties of types F_4, E_6 and E_7). Let k be a field of characteristic not 2 and 3. Let G be an exceptional simple algebraic group of type F_4, inner type E_6 or E_7 with trivial Tits algebras. Let X be a projective G-homogeneous variety. If G is of type E_7 we assume in addition that the respective parabolic subgroup is of type P_7. The main result of the paper says that the degree map on the group of zero cycles of X is injective.