Idempotent completions of equivariant matrix factorization categories

TL;DR

This paper proves that equivariant matrix factorization categories for henselian local hypersurface rings are idempotent complete, extending Dyckerhoff's non-equivariant result to the equivariant setting.

Contribution

It generalizes Dyckerhoff's result by establishing idempotent completeness for equivariant matrix factorization categories.

Findings

Equivariant matrix factorization categories are idempotent complete for henselian local hypersurface rings.

The result extends non-equivariant cases to equivariant settings.

Provides a foundation for further study of equivariant categories in algebraic geometry.

Abstract

We prove that equivariant matrix factorization categories associated to henselian local hypersurface rings are idempotent complete, generalizing a result of Dyckerhoff in the non-equivariant case.