Witt groups of Grassmann varieties

Paul Balmer (1) , Baptiste Calmès (2)

1 Department of Mathematics [UCLA]
2 LML - Laboratoire de Mathématiques de Lens

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.

Domaines: Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Paul Balmer, Baptiste Calmès. Witt groups of Grassmann varieties. 2008. ⟨hal-00424548⟩