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  1. Equivariant homotopy and cohomology theory
  2. Difference Algebra
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Cheer, A. Ismail, Mourad E. Zuhair; Zayed, Ahmed I. Grinberg, Eric L. Marcantognini, S. Deodhar, Vinay Ed. Adem, Alejandro; Milgram, R. James; Ravenel, Douglas C. Richards, Donald P. H9 H Brumfiel, G. Abhyankar, Shreeram S. Walters, Peter Ed. Bokut', L. Gerstenhaber, Murray; Stasheff, Jim Eds.

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Equivariant homotopy and cohomology theory

Gotay, Mark; Moncrief, Vincent E. Cenkl, Mila; Miller, Haynes Eds. Mal'cev Obra en 3 Vols. QA I57 Keyes, David E. Fuchs, L. Abelian groups and noncommutative rings: a collection of papers in memory of Robert B. Warfield, Jr. QA A Graef, John R. Oliker, Vladimir; Treibergs, Andrejs Eds.

Difference Algebra

Dennis, R. Sally, Paul J. Thomas; Ferguson, Thomas S. A1 A57 Haile, Darrell E. Kleiman, Steven L. Enumerative algebraic geometry : proceedings of the Zeuthen Symposium. Kloeden, Peter E. Feingold, Alex J.

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Algebraic geometry: Sundance We study the interplay between the notions of n -coherent rings and finitely n -presented modules, and also study the relative homological algebra associated to them. We show that the n -coherency of a ring is equivalent to the thickness of the class of finitely n -presented modules.

The relative homological algebra part comes from the study of orthogonal complements to this class of modules with respect to the Ext and Tor functors. We also construct cotorsion pairs from these orthogonal complements, allowing us to provide further characterizations of n -coherent rings. We construct Abelian model structures on the category of chain complexes over a ring R , from the notion of homological dimensions of modules.

Using this result, we prove that there is a unique Abelian model structure on the category of chain complexes over R , where the exact complexes are the trivial objects and the complexes with projective dimension at most n form the class of trivially cofibrant objects. In a previous work by D.

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Bravo et. We extend this result by finding a new Abelian model structure with the same trivial objects where the cofibrant objects are given by the class of complexes whose terms are modules with projective dimension at most n. We also prove similar results concerning flat dimension. This monograph provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. We show how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure.

The first part of the monograph introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M.

The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categories known as Gorenstein categories. As self-contained as possible, this monographs presents new results in relative homological algebra and model category theory. We also re-prove some established results using different arguments or from a pedagogical point of view.

In addition, we prove folklore results that are difficult to locate in the literature. Marco A. Research Talks Teaching Travel More. Description of my research field My work focuses mainly on category theory and homological algebra, specifically on the relation between cotorsion theories and abelian model structures, the study of properties of such structures, applications, and the process of obtaining them in different contexts, such as relative homological algebra, Auslander-Buchweitz approximation theory, finiteness conditions of modules, etc.

In a more precise way, my work can be described in the following research lines: Construction of abelian model structures from homological dimensions : The relation between cotorsion theories and model structures is described by a result known as the Hovey Correspondence , which I used in my Ph. Finiteness conditions : I also work on finiteness conditions over rings. With Mindy Huerta and Octavio Mendoza.

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Model structures and relative Gorenstein flat modules and chain complexes. With Sergio Estrada and Alina Iacob. Proceedings of the Edinburgh Mathematical Society. In press. Relative FP-injective and FP-flat complexes and their model structures. With Tiwei Zhao. Communications in Algebra.