On Hilbert's Zyzygys, bigrade modules and local cohomology

• Grant number: 18/05268-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 25, 2019
• End date: 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
• Host 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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FREITAS, T. H.; JORGE PEREZ, V. H.; WIEGAND, R.; WIEGAND, S.. VANISHING OF TOR OVER FIBER PRODUCTS. Proceedings of the American Mathematical Society, v. 149, n. 5, p. 1817-1825, MAY 2021. (18/05268-5, 18/05271-6)