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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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Resolution of singularities of pairs preserving semi-simple normal crossings
TL;DR: In this article, the authors construct a composition of blowings-up f: X' -> X such that the transformed pair (X',D') is everywhere semi-simple normal crossings, and f is an isomorphism over the semi-simple normal crossings locus of (X,D).
Dissertation
Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic
TL;DR: In this paper, the authors argue that there are important philosophical lessons to be learned from the results of Dummett's analysis of choice operators in classical and intuitionistic logic, and they provide a finer-grained basis for their contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions.
Journal ArticleDOI
Upper semi-continuity of the Hilbert-Kunz multiplicity
TL;DR: In this article, the Hilbert-Kunz multiplicity is upper semi-continuous in F-finite rings and algebras of essentially finite type over an excellent local ring.
Posted Content
Some Constacyclic Codes over Finite Chain Rings
TL;DR: It is proved that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes, which allows us to simplify the structure of some constacylic codes.
Posted Content
The relative Breuil-Kisin classification of $p$-divisible groups and finite flat group schemes
TL;DR: In this article, the authors construct an anti-equivalence of categories between the categories of $p$-divisible groups over $R$ and certain semi-linear algebra objects which generalise $(\varphi,\mathfrak{S})$-modules of height $\leqslant1$ (or Kisin modules).
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: