Incompressibility of quadratic Weil transfer of generalized Severi-Brauer varieties

TL;DR

This paper investigates the properties of a variety obtained via Weil transfer from generalized Severi-Brauer varieties, focusing on canonical dimension, incompressibility, and motivic indecomposability, with specific results on canonical 2-dimension.

Contribution

It provides new results on the canonical 2-dimension, incompressibility, and motivic indecomposability of Weil transfer varieties related to generalized Severi-Brauer varieties.

Findings

Determined the canonical 2-dimension of the variety

Established conditions for incompressibility

Analyzed motivic indecomposability in specific cases

Abstract

Let X be the variety obtained by the Weil transfer with respect to a quadratic separable field extension of a generalized Severi-Brauer variety. We study (and, in some cases, determine) the canonical dimension, incompressibility, and motivic indecomposability of X. We determine the canonical 2-dimension of X (in the general case).