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MOTIVIC EULER CHARACTERISTICS AND WITT-VALUED CHARACTERISTIC CLASSES

  • MARC LEVINE (a1)

Abstract

This paper examines Euler characteristics and characteristic classes in the motivic setting. We establish a motivic version of the Becker–Gottlieb transfer, generalizing a construction of Hoyois. Making calculations of the Euler characteristic of the scheme of maximal tori in a reductive group, we prove a generalized splitting principle for the reduction from $\operatorname{GL}_{n}$ or $\operatorname{SL}_{n}$ to the normalizer of a maximal torus (in characteristic zero). Ananyevskiy’s splitting principle reduces questions about characteristic classes of vector bundles in $\operatorname{SL}$ -oriented, $\unicode[STIX]{x1D702}$ -invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\operatorname{SL}_{2}$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, and then generalize this to develop a general calculus of characteristic classes with values in Witt cohomology.

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Marc Levine would like to thank the DFG for its support through the SFB Transregio 45 and the SPP 1786 “Homotopy theory and algebraic geometry”.

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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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