Artin shapes

Nikita Karpenko and Guangzhao Zhu

Vol. 344 (2026), No. 2, 359–366

DOI: 10.2140/pjm.2026.344.359

Abstract

We introduce, and study examples of, a notion of the Artin shape for a motive related to a projective homogeneous variety. We apply it to the problem of finding the complete motivic decomposition of the variety. Our examples cover unitary involution varieties as well as some varieties given by a quadratic Weil transfer. Some of the decompositions obtained dispel prior expectations on how motivic decompositions of projective homogeneous varieties can look like.

Keywords

affine algebraic groups, projective homogeneous varieties, Chow rings and motives

Mathematical Subject Classification

Primary: 14C25, 20G15

Milestones

Received: 17 January 2026

Revised: 25 June 2026

Accepted: 26 June 2026

Published: 8 September 2026