The algebraic theory of fuchsian singularties

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.