Witt groups of Grassmann varieties

TL;DR

This paper computes the total Witt groups of split Grassmann varieties over any regular base, revealing a free module structure with an explicit basis indexed by even Young diagrams.

Contribution

It provides the first explicit basis for the total Witt groups of Grassmann varieties, generalizing previous results to arbitrary regular bases.

Findings

Total Witt groups form a free module over the base's Witt ring.

Explicit basis indexed by even Young diagrams is constructed.

Results apply to any regular base, broadening applicability.

Abstract

We compute the total Witt groups of (split) Grassmann varieties, over any regular base X. The answer is a free module over the total Witt ring of X. We provide an explicit basis for this free module, which is indexed by a special class of Young diagrams, that we call even Young diagrams.