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Algebraic K-Theory of Rings of Integers in Local and Global Fields
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The problem of computing the higher K-theory of a number field F, and of its rings of integers OF, has a rich history as mentioned in this paper, and the resolutions of many of these conjectures by Suslin, Voevodsky, Rost and others have finally made it possible to describe the groups K∗(OF ).Abstract:
The problem of computing the higher K-theory of a number field F , and of its rings of integers OF , has a rich history. Since 1972, we have known that the groups Kn(OF ) are finitely generated [48], and known their ranks [7], but have only had conjectural knowledge about their torsion subgroups [33, 34, 5] until 1997 (starting with [76]). The resolutions of many of these conjectures by Suslin, Voevodsky, Rost and others have finally made it possible to describe the groups K∗(OF ). One of the goals of this survey is to give such a description; here is the odd half of the answer (the integers wi(F ) are even, and are defined in section 3):read more
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Journal Article
The On-Line Encyclopedia of Integer Sequences.
TL;DR: The On-Line Encyclopedia of Integer Sequences (OEIS) as mentioned in this paper is a database of 13,000 number sequences and is freely available on the Web (http://www.att.com/~njas/sequences/) and is widely used.
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The On-Line Encyclopedia of Integer Sequences
TL;DR: The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
Book
Introduction to Homological Algebra
TL;DR: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician as discussed by the authors, which is suitable for second or third year graduate students.
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.
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Algebraic Number Theory
TL;DR: In this paper, Algebraic integral integers, Riemann-Roch theory, Abstract Class Field Theory, Local Class Field theory, Global Class Field and Zeta Functions are discussed.