A motivation for some local cohomologies
Ricardo Garcia Lopez
TL;DR
This paper explores how results from Nori and Ivorra can be used to define motivic versions of Lyubeznik numbers, providing a new perspective on local cohomology invariants and their potential additional structures.
Contribution
It introduces motivic analogues of Lyubeznik numbers using recent developments in motives and discusses possible extra structures on local cohomology modules.
Findings
Motivic Lyubeznik numbers can be defined using Nori and Ivorra's results.
Potential additional structures on local cohomology modules are discussed.
The paper is mainly expository, expanding on previous talks.
Abstract
We explain how some results of M. Nori (on motives) and F. Ivorra (on perverse motives) can be used to define "motivic" versions of Lyubeznik numbers, a set of numerical invariants for local rings. We also discuss on additional structures that might be put on some local cohomology modules (besides those of D- or F-module). This note is mainly expository, it is an expanded version of my talk at the FACARD workshop in Barcelona, on January 2019.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation