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Titlebook: Algebraic K-Theory: Connections with Geometry and Topology; J. F. Jardine,V. P. Snaith Book 1989 Springer Science+Business Media Dordrecht

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期刊全称Algebraic K-Theory: Connections with Geometry and Topology
影响因子2023J. F. Jardine,V. P. Snaith
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学科分类Nato Science Series C:
图书封面Titlebook: Algebraic K-Theory: Connections with Geometry and Topology;  J. F. Jardine,V. P. Snaith Book 1989 Springer Science+Business Media Dordrecht
影响因子A NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; i
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,Some Conjectures on the Algebraic K-Theory of Fields, I: K-Theory with Coefficients and Étale K-Theto conjecturing that ordinary K-theory injects into étale K-theory, or that Bott elements are nonzero divisors in the former. Given the conjectural homomorphisms above, this would also be a formal consequence of the existence of a spectral sequence from étale cohomology to ordinary K-theory, as conj
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On the Naturality of Pic, SK0 and SK1, over a field k, then Pic(A), SK.(A) and SK.(A) are naturally modules over the ring W(k) of Witt vectors over k. If A is any commutative ring, NPic(A), NSK.(A) and NSK.(A) are naturally modules over W(A). The K-theory transfer map, defined when B is an A-algebra which is a finite projective A-module
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Class Numbers, Units and K2,of units of an algebraic number field on one side, and the order and the structure of the 2-primary subgroup of the Milnor K-group over the ring of integers of the number field on the other side..This relates to the Birch-Tate conjecture and a classical question on Sophie Germain primes.
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,Some Conjectures on the Algebraic K-Theory of Fields, I: K-Theory with Coefficients and Étale K-Theom the former towards the latter (Chern classes) and b) comparison with étale K-theory, which is the abutment of a spectral sequence starting with étale cohomology groups. The main theme of this paper is to explain that, locally for the Zariski topology, there should be homomorphisms in the opposite
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