arXiv Open Access 2019

Batalin-Vilkovisky formalism in the $p$-adic Dwork theory

Dohyeong Kim Jeehoon Park Junyeong Park

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Abstrak

The goal of this article is to develop BV (Batalin-Vilkovisky) formalism in the $p$-adic Dwork theory. Based on this formalism, we explicitly construct a $p$-adic dGBV algebra (differential Gerstenhaber-Batalin-Vilkovisky algebra) for a smooth projective complete intersection variety $X$ over a finite field, whose cohomology gives the $p$-adic Dwork cohomology of $X$, and its cochain endomorphism (the $p$-adic Dwork Frobenius operator) which encodes the information of the zeta function $X$. As a consequence, we give a modern deformation theoretic interpretation of Dwork's theory of the zeta function of $X$ and derive a formula for the $p$-adic Dwork Frobenius operator in terms of homotopy Lie morphisms and the Bell polynomials.

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Penulis (3)

Dohyeong Kim

Jeehoon Park

Junyeong Park

Format Sitasi

APA MLA BibTeX

Kim, D., Park, J., Park, J. (2019). Batalin-Vilkovisky formalism in the $p$-adic Dwork theory. https://arxiv.org/abs/1906.06564

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓