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Iwasawa Theory 2012

Author: Athanasios Bouganis
Publisher: Springer
ISBN: 3642552455
Size: 63.33 MB
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This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).

Primes And Knots

Author: Toshitake Kohno
Publisher: American Mathematical Soc.
ISBN: 0821834568
Size: 45.34 MB
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This volume deals systematically with connections between algebraic number theory and low-dimensional topology. Of particular note are various inspiring interactions between number theory and low-dimensional topology discussed in most papers in this volume. For example, quite interesting are the use of arithmetic methods in knot theory and the use of topological methods in Galois theory. Also, expository papers in both number theory and topology included in the volume can help a wide group of readers to understand both fields as well as the interesting analogies and relations that bring them together.

Aspects Of Galois Theory

Author: Helmut Voelklein
Publisher: Cambridge University Press
ISBN: 9780521637473
Size: 48.41 MB
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Collection of articles by leading experts in Galois theory, focusing on the Inverse Galois Problem.

Boundary Cohomology Of Shimura Varieties Iii

Author: Michael Harris
Publisher: Societe Mathematique De France
ISBN: 9782856291078
Size: 69.40 MB
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In this article, third of a series, we complete the verification of the following fact. The nerve spectral sequence for the cohomology of the Borel-Serre boundary of a Shimura variety Sh is a spectral sequence of mixed Hodge-de Rham structures over the field of definition of its canonical model. To achieve that, we develop the machinery of automorphic vector bundles on mixed Shimura varieties, for the latter enter in the boundary of the toroidal compactifications of Sh: and study the nerve spectral sequence for the automorphic vector bundles and the toroidal boundary. We also extend the technique of averting issues of base-change by taking cohomology with growth conditions. We give and apply formulas for the Hodge gradation of the cohomology of both Sh and its Borel-Serre boundary.

Arithmetic And Geometry

Author: Luis Dieulefait
Publisher: Cambridge University Press
ISBN: 1107462541
Size: 11.27 MB
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The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.