Motivic Gauss-Bonnet formulas

被引：16

作者：

Levine, Marc ^{[1
]}

Raksit, Arpon ^{[2
]}

机构：

[1] Univ Duisburg Essen, Fak Math, Essen, Germany

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

ALGEBRA & NUMBER THEORY | 2020年 / 14卷 / 07期

关键词：

motivic homotopy theory; Chow ring; Euler characteristics; hermitian K-theory; COHOMOLOGY THEORIES; K-THEORY;

D O I：

10.2140/ant.2020.14.1801

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The apparatus of motivic stable homotopy theory provides a notion of Euler characteristic for smooth projective varieties, valued in the Grothendieck-Witt ring of the base field. Previous work of the first author and recent work of Deglise, Jin and Khan established a motivic Gauss-Bonnet formula relating this Euler characteristic to pushforwards of Euler classes in motivic cohomology theories. We apply this formula to SL-oriented motivic cohomology theories to obtain explicit characterizations of this Euler characteristic. The main new input is a uniqueness result for pushforward maps in SL-oriented theories, identifying these maps concretely in examples of interest.

引用

页码：1801 / 1851

页数：51

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