Exact subcategories, subfunctors of $\mathrm{Ext}$, and some applications

Abstract

Let $(\mathcal{A},\mathcal{E})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${\mathrm{Ext}}_{\mathcal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in details, and find a range of applications from detecting regularity to understanding Ulrich modules.

To appear in Nagoya Mathematical Journal. This arXiv version contains one additional result (than the Journal Version), namely Proposition 5.1.27

References in corpus (3)

• The trace of the canonical module
• Classifications of exact structures and Cohen-Macaulay-finite algebras
• Relations for Grothendieck groups and representation-finiteness

Cited by in corpus (1)

• Tensor products of $d$-fold matrix factorizations