On the cohomology of the Lubin-Tate curve of level 2 and the Lusztig theory over finite rings

TL;DR

This paper explores the relationship between the etale cohomology of certain components of the Lubin-Tate curve of level 2 and Lusztig theory over finite rings, revealing new connections in arithmetic geometry.

Contribution

It establishes a link between the cohomology of Lubin-Tate curve components and Lusztig theory over finite rings, advancing understanding of their interplay.

Findings

Identifies a relationship between cohomology groups and Lusztig theory.

Provides new insights into the structure of Lubin-Tate curves.

Connects arithmetic geometry with representation theory over finite rings.

Abstract

An etale cohomology group $W$ of some irreducible components, which is the smooth compactification of an affine curve $(X^{q^2}-X)^{q-1}=(Y^{q(q+1)}-Y^{q+1})^{q-1},$ in the stable reduction the Lubin-Tate curve of level two is related to the Lusztig theory over finite rings. In this paper, we investigate a relationship between the cohomology group $W$ and the Lusztig theory.