Formal punctured ribbons and two-dimensional local fields

TL;DR

This paper explores the relationship between formal ribbons on algebraic curves and subspaces of two-dimensional local fields, establishing a correspondence that advances understanding of their geometric and algebraic structures.

Contribution

It introduces a novel correspondence between formal ribbons on curves with additional geometric data and subspaces of two-dimensional local fields.

Findings

Established a one-to-one correspondence between formal ribbons and subspaces of 2D local fields.

Provided a framework connecting geometric data on curves with algebraic structures in local fields.

Enhanced understanding of the structure of formal ribbons in algebraic geometry.

Abstract

We investigate formal ribbons on curves. Roughly speaking, formal ribbon is a family of locally linearly compact vector spaces on a curve. We establish a one-to-one correspondence between formal ribbons on curves plus some geometric data and some subspaces of two-dimensional local field.