Reflexive modules, old and new

Time: 9:30 -- 11:00, July 5th, 2023.

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: Reflexivity is a fundamental notion appearing in many areas of mathematics. Over a commutative ring $R$, an $R$-module $M$ is called reflexive if the natural map from $M$ to $M^{**}$ is an isomorphism, where $M^*$ denote the module of $R$-linear maps from $M$ to $R$. Under mild conditions, reflexivity reduces to the local case of Krull dimension at most one. Despite the classical and elementary nature, the problem of understanding reflexive modules over curve singularities have not been well-understood. I will present many new results in this direction, and sketch connections to trace ideals, $I$-Ulrich modules and Arf singularities.