The algebraic theory of fuchsian singularities

TL;DR

This paper extends the concept of fuchsian singularities to arbitrary characteristic fields, explores their relationships with other mathematical objects, and provides a ring-theoretic characterization along with analysis of their singularity categories and Grothendieck groups.

Contribution

It introduces a generalized definition of fuchsian singularities for any characteristic and offers a new ring-theoretic perspective and categorical analysis.

Findings

Extended fuchsian singularities to arbitrary characteristic fields

Established relationships with other mathematical objects

Analyzed singularity categories and Grothendieck groups

Abstract

This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a purely ring-theoretic characterization of fuchsian singularities. (4) Expoloit their singularity categories and their Grothendieck groups.