Open AccessBook
Smoothness, Regularity and Complete Intersection
Javier Majadas,Antonio G. Rodicio +1 more
- 07 Jun 2010
TL;DR: In this paper, the authors give complete and relatively easy proofs of important results, including the standard results involving localisation of formal smoothness (M. Andre), L. Avramov, some important results of D. Popescu and Andre, and some results from A. Grothendieck's EGA on smooth homomorphisms.
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Abstract: Written to complement standard texts on commutative algebra, this short book gives complete and relatively easy proofs of important results, including the standard results involving localisation of formal smoothness (M. Andre) and localisation of complete intersections (L. Avramov), some important results of D. Popescu and Andre on regular homomorphisms, and some results from A. Grothendieck's EGA on smooth homomorphisms. The authors make extensive use of the Andre–Quillen homology of commutative algebras, but only up to dimension 2, which is easy to construct, and they deliberately avoid using simplicial methods. The book also serves as an accessible introduction to some advanced topics and techniques. The only prerequisites are a basic course in commutative algebra and the first definitions in homological algebra.
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Citations
p −1-Linear Maps in Algebra and Geometry
Manuel Blickle,Karl Schwede +1 more
TL;DR: In this article, a survey of recent developments which grew out of the confluence of Frobenius splitting techniques and tight closure theory is presented, which provide a framework for higher dimension geometry in positive characteristic.
89
On coherent hermitian Witt groups
TL;DR: In this paper, it was shown that the Gersten conjecture holds for coherent hermitian Witt groups of Azumaya algebras with involutions over separated Gorenstein schemes of finite Krull dimension.
14
Simple General Neron Desingularization in local Q-algebras
TL;DR: In this paper, an easier proof of the so-called General Neron Desingularization in the frame of local algebras is given, in the sense that it is shown to be equivalent to the General NER.
8
Direct limits of Cohen–Macaulay rings
TL;DR: In this article, it was shown that A is not necessarily Cohen-Macaulay under various assumptions, but it is a direct limit of a non-affine normal semigroup ring.
7
•Posted Content
A descent theorem for formal smoothness
TL;DR: In this paper, a local homomorphism of noetherian local rings forming part of a commutative square vf=gu is shown to be formally smooth, and conditions on the square which imply that u is formally smooth.
6
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