The Borel character
时间： Thursday 16:30-17:30, 2020-9-17
地点：Zoom Meeting ID: 996 5645 0883；Password: 512464
Abstract: The classical Chern character provides a ring isomorphism between the rational Grothendieck group K_0 and the rational Chow ring of a quasi-projective smooth scheme over a field k. Its construction is based on the existence of Chern classes on both sides and can be explained by the concept of formal groups laws. In recent years, the Chern character has been generalized by J. Riou to provide an isomorphism between the rational K-theory (i.e. the higher K-groups) and the rational total motivic cohomology of a smooth scheme over a field. The purpose of this talk is to explain how one can further generalize Riou’s work in order to get an isomorphism between rational Hermitian K-theory and a generalized version of motivic cohomology.
Jean Fasel is currently full professor at the Université Grenoble-Alpes. He developed the theory of Chow-Witt rings (due to Barge-Morel) and their applications, mainly on the classification of vector bundles. Besides, he is also interested in their connection with algebraic K-theory, Hermitian K-theory and motivic homotopy theory, for example, initiated research in MW-motivic cohomology.
Jean Fasel现任格勒诺布尔-阿尔卑斯大学教授。他在J. Barge和F. Morel的工作基础上发展了Chow-Witt环理论，尤其是专注于其在向量丛分类问题上的应用。他对Chow-Witt环理论与代数K理论，埃尔米特K理论和motivic同伦论的联系上也颇有研究，开创了MW-motivic上同调这一研究方向。