Witt groups of Grassmann varieties
Paul Balmer, Baptiste Calm\`es

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.
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