# l-adic realization of some aspect of Landau-Ginzburg B-models

## TL;DR

This paper explores the algebraic l-adic realization of the Landau-Ginzburg B-models, extending the existing analytic constructions to an algebraic framework for certain Laurent polynomial cases.

## Contribution

It provides an algebraic l-adic realization of Landau-Ginzburg B-models, complementing the existing analytic approaches for specific Laurent polynomial examples.

## Key findings

- Successfully constructed the l-adic realization for algebraic parts of the models.
- Extended the understanding of Landau-Ginzburg B-models in algebraic terms.
- Bridged the gap between analytic and algebraic methods in this context.

## Abstract

The Landau-Ginzburg B-model for a germ of a holomorphic function with an isolated critical point is constructed by K. Saito and finished by M. Saito. Douai and Sabbah construct the Landau-Ginzburg B-models for some Laurent polynomials. The construction relies on analytic procedures, and one can not expect it can be done by purely algebraic method. In this note, we work out the l-adic realization of the algebraic part of the construction.