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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
Citations
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Noetherian rings without finite normalization
Bruce Olberding,B. Olberding +1 more
TL;DR: A number of examples and constructions of local Noetherian domains without finite normalization have been exhibited over the last seventy-five years as discussed by the authors, as well as the theory behind them.
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On deformations of toric Fano varieties
Andrea Petracci,Andrea Petracci +1 more
TL;DR: In this article, the authors collected some results on the deformation theory of toric Fano varieties, and showed that the theory of Fano can be expressed as a deformation problem.
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Image of pseudo-representations and coefficients of modular forms modulo p
TL;DR: In this article, the authors describe the image of general families of two-dimensional representations over compact semi-local rings, and apply this description to the family carried by the universal Hecke algebra acting on the space of modular forms of level N modulo a prime p.
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Ideal-adic completion of quasi-excellent rings (after Gabber)
Kazuhiko Kurano,Kazuma Shimomoto +1 more
TL;DR: In this article, a detailed proof of Gabber's result on lifting of quasi-excellent rings is given, and it is shown that an ideal-adic completion of an excellent ring is also an excellent (resp., quasiexcellent) ring.
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Invariants and separating morphisms for algebraic group actions
Emilie Dufresne,Hanspeter Kraft +1 more
TL;DR: In this paper, a refinement of Winkelmann's work on invariant rings and quotients of algebraic group actions on affine varieties is presented, where they take a more geometric point of view.
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: