Piecewise hereditary algebras under field extensions

TL;DR

This paper proves that the property of being derived equivalent to a hereditary algebra is preserved under finite separable field extensions for finite-dimensional algebras.

Contribution

It establishes an equivalence condition showing that a finite-dimensional algebra's hereditary derived equivalence status remains unchanged under finite separable field extensions.

Findings

Derived equivalence to hereditary algebra is preserved under field extension.

A finite-dimensional algebra is hereditary equivalent if and only if its extension is.

The result applies specifically to finite separable field extensions.

Abstract

Let $A$ be a finite-dimensional $k$-algebra and $K/k$ be a finite separable field extension. We prove that $A$ is derived equivalent to a hereditary algebra if and only if so is $A\otimes_kK$.