Formal local cohomology defined by a pair of idelas

Author(s)

Thiago Henrique de Freitas

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2015-09-28

Examining board members

Victor Hugo Jorge Pérez; Paulo Roberto Brumatti; Eduardo do Nascimento Marcos; Cleto Brasileiro Miranda Neto; Behrooz Mirzaii

• Advisor: Victor Hugo Jorge Pérez

Abstract

In this work we will introduce two generalizations of the concept of formal local cohomology, called formal local cohomology and Cech formal local cohomolgy, both defined by a pair of ideals. We study their behavior in several aspects, such as vanishing and non vanishing, artinianness, finiteness, relations with Matlis dual, and others. Forth is purpose, we use the concept of local cohomology defined by a pair of ideals, introduced in [50]. Also, we analyze the endomorphism ring of the local cohomology defined by a pair of ideal and when the Matlis dual of certain local cohomology defined by a pair of ideals are Cohen-Macaulaymodules. (AU)

• FAPESP's process: 12/01084-0 - Coefficients ideals for arbitrary ideals
• Grantee: Thiago Henrique de Freitas
• Support Opportunities: Scholarships in Brazil - Doctorate