Time: 14:00 - 15:45, December 11, 2024

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

Abstract: Let $(R,m,k)$ be an equicharacteristic one-dimensional complete local domain over an algebraically closed field $k$ of characteristic $0$. R. Berger conjectured that $R$ is regular if and only if the universally finite module of differentials $Omega_R$ is a torsion-free $R$ module. We give new cases of this conjecture by extending works of G"uttes and Corti~{n}as, Geller and Waybill. This is obtained by constructing a new subring $S$ of $Hom_R(m,m)$ and constructing enough torsion in $Omega_S$, enabling us to pull back a nontrivial torsion to $Omega_R$. In the process we also define reduced type which is a finer invariant compared to the Cohen-Macaulay type. One of our goals is to study this invariant for one dimensional rings.

Program of Special Semester on Commutative Algebra