CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Peru
Associate professor (MS-5.3) at the University of São Paulo. Master's at Mathematics from the State University of Campinas (1996) and have PhD from the University of São Paulo-ICMC-USP-São Carlos (1999). He has experience in Mathematics, with emphasis in Commutative Algebra and Complex Singularity Theory, currently researcher in the following sub-areas: Cohomological Algebra; Ext and Tor functors, Local Cohomology of Modules and Local Cohomology of Graduated Modules, Formal Local Cohomology, Cohomological Modular Invariants, Application Germs Complexity, Equivalence of Application Germs, Multiplicity of Ideals and Modules. (Source: Lattes Curriculum)
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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 g…
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 wi…
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. (AU)
(Only some records are available in English at this moment)
This project aims to study the vanishing properties of Tor and Ext derived functors in order to obtain structural, homological or geometric information about modules on commutative rings from homological vanishing properties. There are traditional results of the theory that verify, for example, that if an R-module M satisfies Ext1(M,N)=0, for every R-module N , then M is a projective R-mo…
Let $R$ be a commutative Noetherian ring with unity and $M$ be a finitely generated $R$-module. It is know that if each finitely generated $R$-module $N$ satisfies the condition that the $R$-module $\mbox{Ext}^{i}_R(M,N)$ is the zero module for every integer $i>0$, then $M$ is projective. A question that arises is the following: if such condition holds at least for $N=R$ and $N=M$, is it …
We will present here a research project, extremely broad in commutative algebra and homological algebra, which will be investigated over a two-year master's degree. This project is based on homological algebra theory such as Ext and Tor funkers, local module cohomology. But explicitly, the objective is to explore the structure and algebraic, homological, arithmetic and geometric propertie…
Kishor Shah proved the existence and uniqueness of a chain of ideals between the ideals $ I $ the ring $ R $ and the integral closure of the same, these ideals preserve the first $ k +1$ the Hilbert coefficients of $I$, i.e., there are ideals $I_k $ containing the ideal $I$, for every integer $ k = 1, \ ldots, d $ such that $ I \subset I_ d \subset \ldots \subset I_1 \subset \overline {…
The study of homological dimensions of finitely generated modules over Noetherian local rings and their relationship with the vanishing of the derived functors Tor and Ext has been a topic of intense investigation in recent years. In this project, we aim to investigate the vanishing of the derived functors Tor and Ext and modules of finite quasi-projective dimension. Through this, we hope…
This project aims to investigate the implications of the vanishing of Ext and Tor. One of its objectives is to establish criteria for the freeness of a module over a Noetherian local ring through the vanishing of specific Ext or Tor modules. Special attention is dedicated to cases where the Hom or the tensor product of two particular modules has some finite homological dimension.
In this work, we will go analyse when the Formal Local Cohomology defined by a pair of ideals is an Artinian module and establish conditons of finiteness for this module. (AU)
In recent years, using different sequences, expressed he mixed multiplicity in terms of the Hilbert-Samuel multiplicity, for example, in the case of m-primary ideals, Risler-Teissier in 1973 showed that each mixed multiplicity is the Hilbert-Samuel multiplicity of an ideal generated by a sequence superficial, then this was generalized to m-primary ideals using notions of joint reduction t…
| 6 / 6 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 3 / 3 | Completed scholarships in Brazil |
| 2 / 2 | Ongoing scholarships abroad |
| 3 / 2 | Completed scholarships abroad |
| 16 / 15 | All research grants and scholarships |
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