Local cohomology, homological problems and blowup algebras

• Grant number: 19/21843-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: March 01, 2020
• End date: 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
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos

Abstract

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

(8)

(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)

MIRANDA-NETO, CLETO B.. ullback of the Normal Module of Ideals with Low Codimensio. QUARTERLY JOURNAL OF MATHEMATICS, v. 72, n. 4, SI, p. 1147-1166, DEC 9 2021. (19/21843-2)

JORGE-PEREZ, VICTOR H.; MIRANDA-NETO, CLETO B.. Homological aspects of derivation modules and critical case of the Herzog-Vasconcelos conjecture. COLLECTANEA MATHEMATICA, v. 73, n. 2, p. 17-pg., 2021-02-03. (19/21843-2)

JORGE-PEREZ, VICTOR H.; MIRANDA-NETO, CLETO B.. Criteria for prescribed bound on projective dimension. COMMUNICATIONS IN ALGEBRA, JAN 2021. (19/21843-2)

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. (19/21843-2)

FREITAS, THIAGO H.; JORGE-PEREZ, VICTOR H.; MIRANDA-NETO, CLETO B.; SCHENZEL, PETER. Generalized local duality, canonical modules, and prescribed bound on projective dimension. Journal of Pure and Applied Algebra, v. 227, n. 2, p. 17-pg., 2023-02-01. (19/21843-2)

MIRANDA-NETO, CLETO B.. PULLBACK OF THE NORMAL MODULE OF IDEALS WITH LOW CODIMENSION. QUARTERLY JOURNAL OF MATHEMATICS, v. 72, n. 4, p. 1147-1166, DEC 2021. (19/21843-2)

MIRANDA-NETO, CLETO B.. Maximally differential ideals of finite projective dimension. BULLETIN DES SCIENCES MATHEMATIQUES, v. 166, FEB 2021. (19/21843-2)

JORGE-PEREZ, VICTOR H.; MIRANDA-NETO, CLETO B.. Criteria for prescribed bound on projective dimension. COMMUNICATIONS IN ALGEBRA, v. 49, n. 6, p. 11-pg., 2021-01-16. (19/21843-2)