Open AccessBook
The K-Book: An Introduction to Algebraic K-theory
TLDR
Projective modules and vector bundles The Grothendieck group $K 0$ $K 1$ and $K 2$ of a ring Definitions of higher $K$-theory The fundamental theorems of higher$K$theory as mentioned in this paper.Abstract:
Projective modules and vector bundles The Grothendieck group $K_0$ $K_1$ and $K_2$ of a ring Definitions of higher $K$-theory The fundamental theorems of higher $K$-theory The higher $K$-theory of fields Nomenclature Bibliography Indexread more
Citations
More filters
Book
Graded Rings and Graded Grothendieck Groups
TL;DR: The first systematic account of the graded Grothendieck group, a powerful invariant in algebra which has recently been adopted to classify the Leavitt path algebras, can be found in this paper.
Journal ArticleDOI
La réalisation étale et les opérations de Grothendieck
Joseph Ayoub,Joseph Ayoub +1 more
TL;DR: In this article, the authors construct etale realization functors defined on the categories DAet(X, Λ) of etale motives (without transfers) over a scheme X. Their construction relies on a relative rigidity theorem a la Suslin-Voevodsky that they will establish first.
Journal ArticleDOI
Homological stability for automorphism groups
TL;DR: In this paper, a family of groups admitting a braided monoidal structure is constructed, and the authors show that homological stability holds with both polynomial and abelian twisted coefficients, with no further assumptions.
Journal ArticleDOI
Compactly supported Wannier functions and algebraic K -theory
TL;DR: In this paper, it was shown that for general complex band structures (vector bundles) or general complex complex Hamiltonians (general complex Wannier functions) without additional crystallographic symmetries, with the result that in general the nontrivial bundles that can arise from compactly supported Wernier-type functions are those that may possess, in each of $d$ directions, the nonsmooth winding that can occur in the same symmetry class in one dimension, but nothing else.
References
More filters
Book
Éléments de géométrie algébrique
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
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:
Book
Commutative Ring Theory
Hideyuki Matsumura,Miles Reid +1 more
TL;DR: In this article, the authors introduce the notion of complete local rings and apply it to a wide range of applications, including: I-smoothness, I-flatness revisited, and valuation rings.
Book
A Course in Computational Algebraic Number Theory
TL;DR: The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.
Journal ArticleDOI
On the Structure of Hopf Algebras
John Milnor,John C. Moore +1 more
TL;DR: The structure theorem of Hopf algebras has been generalized by Borel, Leray, and others as discussed by the authors, and some new proofs of the classical theorems are given, as well as some new results.