ON THE RELATION OF SPECIAL LINEAR ALGEBRAIC COBORDISM TO WITT GROUPS

被引：7

作者：

Ananyevskiy, Alexey ^{[1
]}

机构：

[1] St Petersburg State Univ, Chebyshev Lab, 14th Line,29b, St Petersburg 199178, Russia

来源：

HOMOLOGY HOMOTOPY AND APPLICATIONS | 2016年 / 18卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

Witt groups; algebraic cobordism; SL-oriented cohomology; Hopf map;

D O I：

10.4310/HHA.2016.v18.n1.a11

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We reconstruct derived Witt groups via special linear algebraic cobordism. There is a morphism of ring cohomology theories that sends the canonical Thom class in special linear cobordism to the Thom class in the derived Witt groups. We show that for every smooth variety X, this morphism induces an isomorphism MSL eta*[star] (X) circle times ([2 star])(MSL0) ((pt)) W-2 star (pt) -> W-star(X) [eta, eta(-1)], where eta is the stable Hopf map. This result is an analogue of the result by Panin and Walter reconstructing hermitian K-theory using symplectic algebraic cobordism.

引用

页码：205 / 230

页数：26

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