Categorical proof of Holomorphic Atiyah-Bott formula

Abstract

Given a symmetric monoidal $(\infty ,2)$-category $\mathcal{E}$ we promote the trace construction to a functor. We then apply this formalism to the case when $\mathcal{E}$ 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).

arXiv commentFixed metadata. 21 pages. Accepted to Journal of the Institute of Mathematics of Jussieu