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On Hilbert's Zyzygys, bigrade modules and local cohomology

Grant number: 18/05268-5
Support type:Research Grants - Visiting Researcher Grant - International
Duration: March 25, 2019 - April 22, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Victor Hugo Jorge Pérez
Grantee:Victor Hugo Jorge Pérez
Visiting researcher: Roger Allen Wiegand
Visiting researcher institution: University of Nebraska-Lincoln (UNL), United States
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

We will present here two research projects that will be developed through the visit of the Professors Roger Wiegand and Sylvia Weigand to ICMC-USP. These projects have as pillars the theory of multiplicities and the theory of local cohomology. The first project proposal deals with an extension of Hilbert's famous Syzygy Theorem for cofinite modules. As a consequence of this project, it will be possible to show some cases where the local cohomology has finite projective dimension and more, it will be possible to explain such value. The second proposal of work is based on the investigation of the Hilbert coefficients of the local cohomology when approached with a bigraduada structure. We aim here to show that the first Hilbert coefficient of the i-th local large cohomology has a polynomial behavior and more, the degree of such a polynomial is limited by i. Obtaining such a result will open up a range of underlying investigations, thus making such a project a potential future quote. (AU)