Categorical proof of Holomorphic Atiyah-Bott formula
- Resource Type
- Working Paper
- Authors
- Kondyrev, Grigory; Prikhodko, Artem
- Source
- Subject
- Mathematics - Algebraic Geometry
Mathematics - Category Theory
- Language
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).
Comment: Fixed metadata. 21 pages. Accepted to Journal of the Institute of Mathematics of Jussieu