Batalin-Vilkovisky formalism in the $p$-adic Dwork theory
Abstract
The goal of this article is to develop BV (Batalin-Vilkovisky) formalism in the -adic Dwork theory. Based on this formalism, we explicitly construct a -adic dGBV algebra (differential Gerstenhaber-Batalin-Vilkovisky algebra) for a smooth projective complete intersection variety over a finite field, whose cohomology gives the -adic Dwork cohomology of , and its cochain endomorphism (the -adic Dwork Frobenius operator) which encodes the information of the zeta function . As a consequence, we give a modern deformation theoretic interpretation of Dwork's theory of the zeta function of and derive a formula for the -adic Dwork Frobenius operator in terms of homotopy Lie morphisms and the Bell polynomials.
Keywords
Cite
@article{arxiv.1906.06564,
title = {Batalin-Vilkovisky formalism in the $p$-adic Dwork theory},
author = {Dohyeong Kim and Jeehoon Park and Junyeong Park},
journal= {arXiv preprint arXiv:1906.06564},
year = {2021}
}
Comments
23 pages; this second version is a major revision of the first version in the sense that its main emphasis moves to the interplay between physical theory (BV formalism) and number theory (Dwork theory of zeta functions)