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Local cohomology, homological problems and blowup algebras

Grant number: 19/21843-2
Support type:Research Grants - Visiting Researcher Grant - Brazil
Duration: March 01, 2020 - February 28, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Victor Hugo Jorge Pérez
Grantee:Victor Hugo Jorge Pérez
Visiting researcher: Cleto Brasileiro Miranda Neto
Visiting researcher institution: Universidade Federal da Paraíba (UFPB). Centro de Ciências Exatas e da Natureza (CCEN), Brazil
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil


This comprehensive project proposes groundbreaking research on current topics of major relevance in commutative algebra and related areas, focusing on:Study local cohomology modules and their variations, in all their aspects.We will also explore the structure and algebraic, homological, arithmetic and geometric properties of finely generated modules and their blowup algebras. One of the goals is to study special module classes, the depth formula for tensor products, the Auslander-Reiten conjecture, and the impact of the finitude of various homological dimensions. For more details see in the proposed project. (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)
JORGE-PEREZ, VICTOR H.; MIRANDA-NETO, CLETO B. Homological aspects of derivation modules and critical case of the Herzog-Vasconcelos conjecture. COLLECTANEA MATHEMATICA, FEB 2021. Web of Science Citations: 0.
MIRANDA-NETO, CLETO B. Maximally differential ideals of finite projective dimension. BULLETIN DES SCIENCES MATHEMATIQUES, v. 166, FEB 2021. Web of Science Citations: 0.
JORGE-PEREZ, VICTOR H.; MIRANDA-NETO, CLETO B. Criteria for prescribed bound on projective dimension. COMMUNICATIONS IN ALGEBRA, JAN 2021. Web of Science Citations: 0.

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