Witt groups of spinor varieties

TL;DR

This paper provides a combinatorial presentation of Witt groups for spinor varieties using even shifted Young diagrams, employing advanced algebraic geometry techniques like blow-up setups and localization sequences.

Contribution

It introduces a novel combinatorial description of Witt groups of spinor varieties, extending existing geometric methods with new formulas and homomorphism analyses.

Findings

Witt groups of spinor varieties can be described by even shifted Young diagrams.

The paper connects geometric formulas with combinatorial objects.

It advances understanding of Witt groups in algebraic geometry.

Abstract

We show that Witt groups of spinor varieties (aka.\ maximal isotropic Grassmannians) can be presented by combinatorial objects called even shifted young diagram. Our method relies on the Blow-up setup of Balmer-Calm\`es, and we investigate the connecting homomorphism of the localization sequence via the projective bundle formula of Walter-Nenashev, the projection formula of Calm\`es-Hornbostel and the excess intersection formula of Fasel.