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Towards a Modulo $p$ Langlands Correspondence for GL$_2$

2012-02-22 Mathematics
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Release : 2012-02-22
Genre : Mathematics
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Book Synopsis Towards a Modulo $p$ Langlands Correspondence for GL$_2$ by : Christophe Breuil

Download or read book Towards a Modulo $p$ Langlands Correspondence for GL$_2$ written by Christophe Breuil. This book was released on 2012-02-22. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.

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Download or read book written by . This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

The Local Langlands Conjecture for GL(2)

2006-08-29 Mathematics
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Release : 2006-08-29
Genre : Mathematics
Kind : eBook
Book Rating : 11X/5 ( reviews)

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Book Synopsis The Local Langlands Conjecture for GL(2) by : Colin J. Bushnell

Download or read book The Local Langlands Conjecture for GL(2) written by Colin J. Bushnell. This book was released on 2006-08-29. Available in PDF, EPUB and Kindle. Book excerpt: The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.

Automorphic Forms on GL (2)

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 127/5 ( reviews)

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Book Synopsis Automorphic Forms on GL (2) by : H. Jacquet

Download or read book Automorphic Forms on GL (2) written by H. Jacquet. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in the Theory of Numbers

2015-10-28 Mathematics
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Release : 2015-10-28
Genre : Mathematics
Kind : eBook
Book Rating : 012/5 ( reviews)

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Book Synopsis Advances in the Theory of Numbers by : Ayşe Alaca

Download or read book Advances in the Theory of Numbers written by Ayşe Alaca. This book was released on 2015-10-28. Available in PDF, EPUB and Kindle. Book excerpt: The theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as discrete mathematics, cryptography, and coding theory. The proof by Andrew Wiles (with Richard Taylor) of Fermat’s last theorem published in 1995 illustrates the high level of difficulty of problems encountered in number-theoretic research as well as the usefulness of the new ideas arising from its proof. The thirteenth conference of the Canadian Number Theory Association was held at Carleton University, Ottawa, Ontario, Canada from June 16 to 20, 2014. Ninety-nine talks were presented at the conference on the theme of advances in the theory of numbers. Topics of the talks reflected the diversity of current trends and activities in modern number theory. These topics included modular forms, hypergeometric functions, elliptic curves, distribution of prime numbers, diophantine equations, L-functions, Diophantine approximation, and many more. This volume contains some of the papers presented at the conference. All papers were refereed. The high quality of the articles and their contribution to current research directions make this volume a must for any mathematics library and is particularly relevant to researchers and graduate students with an interest in number theory. The editors hope that this volume will serve as both a resource and an inspiration to future generations of researchers in the theory of numbers.

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