Corpus ID: 115974126

Commutative Algebra: Chapters 1-7

  title={Commutative Algebra: Chapters 1-7},
  author={Nicolas Bourbaki},
Categorical and homological aspects of module theory over commutative rings
The purpose of this work is to understand the structure of the subcategories of mod(R) and the derived category D(R) for a commutative Noetherian ring R. Special focus is given to categoriesExpand
Quaternion Algebras with the Same Subfields
Prasad and Rapinchuk asked if two quaternion divisionF-algebras that have the same subfields are necessarily isomorphic. The answer is known to be “no” for some very large fields. We prove that theExpand
Smooth and irreducible multigraded Hilbert schemes
Abstract The multigraded Hilbert scheme parametrizes all homogeneous ideals in a polynomial ring graded by an abelian group with a fixed Hilbert function. We prove that any multigraded Hilbert schemeExpand
For a division algebra D finite dimensional over its center Z(D) = F , it is a conjecture that CK1(D) := Coker(K1F → K1D) is trivial if and only if D ∼= ( F ) with F a formally real PythagoreanExpand
Punctually free ideals
Let I be a nonzero f.g. PF ideal. We have seen that I is invertible iff it is regular, and I is projective iff rk I is constant on a nhbd of each prime; thus, such an I is invertible iff it is aExpand
Artin Groups and Iwahori-Hecke algebras over finite fields
In this doctoral thesis, we will determine the image of Artin groups associated to all finite irreducible Coxeter groups inside their associated finite Iwahori-Hecke algebra. This was done in typeExpand
Uma Generalizacão do Teorema de Serre-Swan
In the present work we will study a generalization of the classical theorems of Serre and Swan. We will determine the class of ringed spaces (X,OX), so that the category of locally free sheaves ofExpand
Images of Galois representations associated to p-adic families of modular forms
Author(s): Lang, Jaclyn Ann | Advisor(s): Hida, Haruzo | Abstract: Ribet and Momose described the effect of extra twists on the image of Galois representations associated to classical modular formsExpand
Characterization of finite extensions / Caractérisation des extensions finies
In this note we are interested in finite extensions. In addition, we give a necessary and sufficient condition for that a separable extension be finite.  Also, by means of invariant we characterizeExpand