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Categorical proof of Holomorphic Atiyah-Bott formula

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arxiv 1607.06345 v3 pith:ZSJNDU5S submitted 2016-07-21 math.AG math.CT

Grigory Kondyrev , Artem Prikhodko This is my paper · ORCID
classification math.AGmath.CT
keywords formulaatiyah-bottcategoricalcategoryholomorphicinftymathscrproof
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abstract

Given a symmetric monoidal $(\infty,2)$-category $\mathscr E$ we promote the trace construction to a functor. We then apply this formalism to the case when $\mathscr{E}$ is the $(\infty,2)$-category of $k$-linear presentable categories which in combination of various calculations in the setting of derived algebraic geometry gives a categorical proof of the classical Atiyah-Bott formula (also known as the Holomorphic Lefschetz fixed point formula).

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  1. A toy model for the Drinfeld-Lafforgue shtuka construction

    math.AG 2019-08 conditional novelty 7.0 of 10

    In a Betti/topological setting, applying categorical and 2-categorical traces to a Hecke action yields universal shtukas, excursion operators, and an S=T identity.

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