Categorical proof of Holomorphic AtiyahBott formula
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 AtiyahBott formula (also known as the Holomorphic Lefschetz fixed point formula).
 Publication:

arXiv eprints
 Pub Date:
 July 2016
 arXiv:
 arXiv:1607.06345
 Bibcode:
 2016arXiv160706345K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Category Theory
 EPrint:
 Fixed metadata. 21 pages. Accepted to Journal of the Institute of Mathematics of Jussieu