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A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula

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arxiv 1309.6147 v3 pith:7MLC5KKL submitted 2013-09-24 math.AG math.ATmath.KT

Marc Hoyois This is my paper · ORCID
classification math.AGmath.ATmath.KT
keywords traceringschemebasecharacteristicclassetaleeuler
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We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the "Euler characteristic integral" of a certain cohomotopy class over its scheme of fixed points. When the base is a field and the fixed points are \'etale, we compute this integral in terms of Morel's identification of the ring of endomorphisms of the motivic sphere spectrum with the Grothendieck-Witt ring. In particular, we show that the Euler characteristic of an \'etale algebra corresponds to the class of its trace form in the Grothendieck-Witt ring.

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  1. Iterated traces in 2-categories and Lefschetz theorems

    math.AT 2019-08 conditional novelty 7.0 of 10

    Iterated traces in any 2-dualizable symmetric monoidal bicategory commute, recovering and extending a wide family of Lefschetz-type theorems.

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