Zero cycles on projective varieties and the norm principle

TL;DR

This paper applies the Gille-Merkurjev norm principle to compute the degree map images for various algebraic varieties, including quadrics and exceptional groups, unifying several classical results in algebraic geometry.

Contribution

It provides a uniform approach to compute the degree map images for quadrics, orthogonal Grassmannians, and exceptional varieties, extending known theorems.

Findings

Computed the degree map image for quadrics (Springer's theorem)

Extended the norm principle to twisted forms of orthogonal Grassmannians

Applied the method to E6 and E7 varieties, confirming Rost's theorem

Abstract

Using the Gille-Merkurjev norm principle we compute in a uniform way the image of the degree map for quadrics (Springer's theorem), for twisted forms of maximal orthogonal Grassmannians (theorem of Bayer-Fluckiger and Lenstra), for E6- (Rost's theorem), and E7-varieties.