The derived-discrete algebras and standard equivalences

TL;DR

This paper proves that all derived equivalences between derived-discrete algebras of finite global dimension are standard, meaning they are given by derived tensor functors with tilting complexes.

Contribution

It establishes that such derived equivalences are always isomorphic to derived tensor functors, confirming a conjecture for this class of algebras.

Findings

All derived equivalences between these algebras are standard.

Derived equivalences are isomorphic to tensor functors with tilting complexes.

Supports the conjecture for derived-discrete algebras of finite global dimension.

Abstract

We prove that any derived equivalence between derived-discrete algebras of finite global dimension is standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex.