Tuesday, November 18, 14:00, 7.527.

Erlend Børve (University of Graz)
tau-tilting theory and tau-tilting finiteness under scalar extension.

Abstract:
Let L:k be a field extension and let A be a finite-dimensional k-algebra. The extension of scalars of A along L:k is the L-algebra A^L, obtained by tensoring A and L over k.

In the early 1980s, Jensen and Lenzing showed that extension of scalars preserves many module-theoretic and homological properties, particularly when L:k is MacLane separable. In particular, representation-finiteness is preserved in this case. However, if A is tau-tilting finite, i.e. it admits only a finite number of support tau-tilting modules up to isomorphism, this need not be true for A^L. We explore some examples and counter-examples of when tau-tilting finiteness is preserved. Along the way, we explain how tau-tilting theory and related notions lift under extension of scalars. The talk is based on joint work in progress with Max Kaipel (Cologne).