Browsing by Author "Iyengar, Srikanth B."

Now showing 1 - 4 of 4
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    Asymptotic Phenomena in Local Algebra and Singularity Theory
    (Zürich : EMS Publ. House, 2016) Cutkosky, Steven Dale; Iyengar, Srikanth B.
    The goal of this workshop was to highlight, and further, the interactions between local algebra and singularity theory. The timing was serendipitous for both subjects have witnessed tremendous progress recently, much of which was reported at the workshop.
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    Module categories for group algebras over commutative rings
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Benson, Dave; Iyengar, Srikanth B.; Krause, Henning; Stevenson, Greg
    We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits of weakly injective modules. There is also an analogous version of the homotopy category of weakly injective kG-modules and a recollement relating the stable category, the homotopy category, and the derived category of kG-modules.
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    Resolutions in Local Algebra and Singularity Theory
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2023) Conca, Aldo; Cutkosky, Steven Dale; Faber, Eleonore; Iyengar, Srikanth B.
    Commutative algebra is a vast subject, with connections to many different areas of mathematics, and beyond. The focus of this workshop was on three areas, all concerned with resolutions in various forms. One is the resolution of singularities of algebraic varieties, which remains a vibrant topic of research. The second is the theory of noncommutative resolution of singularities. Introduced two decades ago, this subject has witnessed remarkable growth developing connections to algebraic geometry, commutative algebra, cluster algebras, and the representation theory of algebras, both commutative and noncommutative, among others. The third intended meaning of the world "resolution" is as in free resolutions of algebras and modules in commutative algebra. There is another sense in which the title is appropriate: recently three long standing open problems in commutative algebra have been resolved. This workshop brought together experts and early career researchers in these various fields, to facilitate exchange of ideas and to explore potential collaborations.
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    Stratifying modular representations of finite groups
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Benson, Dave; Iyengar, Srikanth B.; Krause, Henning
    We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Along the way we establish similar classifications for differential graded modules over graded polynomial rings, and over graded exterior algebras.