Time: 10:00-11:00  September 2, 2021(Thursday)

Place: MCM410

Title: Split Milnor-Witt Motives

Abstract: The Chow-Witt group is a kind of cohomology theory of smooth varieties which combines Chow groups and quadratic information of fields together. It admits realizations towards singular cohomology of both real and complex points, with significant applications in classifying vector bundles and Hermitian K-theory, as well as a refined version of enumerative geometry.

Recently, B. Calmès, F. Déglise and J. Fasel defined a kind of motivic theory representing the Chow-Witt groups, namely the Milnor-Witt (abbr. MW) motives. It's rationally equivalent to the motivic stable homotopy category defined by F. Morel.

In this talk, we introduce the notion of split MW-motives. Varieties whose MW-motives split have free complex cohomology and only 2-torsions in real cohomology. We compute the MW-motive of Grassmannians bundles and complete flags bundles, which turn out to fit the split pattern we desired. Moreover, some interesting observations of Bockstein cohomology will be presented.