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arXiv · 1607.06345

Categorical proof of Holomorphic Atiyah-Bott formula

Grigory Kondyrev·Artem Prikhodko
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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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Grigory Kondyrev, Artem Prikhodko. 2019-11-12. Categorical proof of Holomorphic Atiyah-Bott formula. https://doi.org/10.1017/s1474748018000543

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