Commutative Algebra Seminar
Cheng Meng
Purdue University
Strongly Lech-independent ideals and Lech's conjecture
Abstract: We introduce the notion of strongly Lech-independent ideals as a generalization of Lech-independent ideals defined by Lech and Hanes, and use this notion to derive inequalities on multiplicities of ideals. In particular we prove that if $(R, \mathfrak{m}) \to (S, \mathfrak{n})$ is a flat local extension of Noetherian local rings with $\dim R=\dim S$, the completion of $(S, \mathfrak{n})$ is the completion of a standard graded ring $(S_g, \mathfrak{n}_g)$ over a field $k$ and the completion of $I=\mathfrak{m}S$ is extended from a homogeneous ideal $I_g$, then $e(R) \leq e(S)$.
Wednesday April 20, 2022 at 3:00 PM in Zoom