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Commutative Algebra I
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A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.Abstract:
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typedread more
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Period-index bounds for arithmetic threefolds
TL;DR: Using Gabber's theory of prime-to-ell$ alterations and the deformation theory of twisted sheaves, the authors showed that the index divides the fourth power of the period for every Brauer class whose period is prime to $6p.
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Generalized differentials and prolongation spaces
TL;DR: In this article, it was shown that the spectrum of [D ] (A, ψ ) B is isomorphic to a prolongation space as defined by Moosa and Scanlon, providing a direct construction of the latter.
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Verification Protocols with Sub-Linear Communication for Polynomial Matrix Operations.
TL;DR: New protocols to verify the correctness of various computations on matrices over the ring F[x] of univariate polynomials over a field F are designed and analyzed to minimize the communication cost.
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Gelfand-Tsetlin variety for $\mathfrak{gl}_n$
TL;DR: In this article, the Gelfand-Tsetlin variety of the Kostant-Wallach map is shown to be equidimensional, i.e. all its irreducible components have the same dimension.
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Weak normalization in graded extensions and weak subintegral closure of ideals
TL;DR: In this paper, the weak normalization of an ideal in a graded extension of commutative rings has been studied and several properties of the weak subintegral closure of the ideal have been proved.
References
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Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures: