Motivic Gauss-Bonnet formulas

被引：15
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.
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收藏
页码：1801 / 1851
页数：51
相关论文
共 40 条
  • [11] ALGEBRAIC CYCLES AND HIGHER K-THEORY[J]. BLOCH, S. ADVANCES IN MATHEMATICS, 1986(03)
  • [12] Calmes B., 2014, PREPRINT
  • [13] Push-forwards for Witt groups of schemes[J]. Calmes, Baptiste;Hornbostel, Jens. COMMENTARII MATHEMATICI HELVETICI, 2011(02)
  • [14] Deglise F., 2018, PREPRINT
  • [15] Dold A., 1978, P INT C GEOM TOP, P81
  • [16] Fasel J, 2008, MEM SOC MATH FR, V113, P1
  • [17] The six operations in equivariant motivic homotopy theory[J]. Hoyois, Marc. ADVANCES IN MATHEMATICS, 2017
  • [18] A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula[J]. Hoyois, Marc. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2014(06)
  • [19] Kharlamov V. M., 1974, FUNCTIONAL ANAL APPL, V8, P50
  • [20] Levine M., 2017, PREPRINT
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