The Local Langlands Correspondence in Singular Families of Representations PDF Download
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Author: Tibor András Backhausz
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Tibor András Backhausz
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Christophe Breuil
Publisher: American Mathematical Soc.
ISBN: 0821852272
Category : Mathematics
Languages : en
Pages : 127
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Book Description
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.
Author: Edward Frenkel
Publisher: Cambridge University Press
ISBN: 0521854431
Category : Mathematics
Languages : en
Pages : 5
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Book Description
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Author: H. Jacquet
Publisher: Springer
ISBN: 3540376127
Category : Mathematics
Languages : en
Pages : 156
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Author: J. Adams
Publisher: Springer Science & Business Media
ISBN: 146120383X
Category : Mathematics
Languages : en
Pages : 331
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Book Description
This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.
Author: Luis Dieulefait
Publisher: Cambridge University Press
ISBN: 1107462541
Category : Mathematics
Languages : en
Pages : 539
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Book Description
The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.
Author: Michael Harris
Publisher: Princeton University Press
ISBN: 0691090920
Category : Mathematics
Languages : en
Pages : 287
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Book Description
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.
Author: Peter Scholze
Publisher: Princeton University Press
ISBN: 0691202095
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
Author: Joseph Bernstein
Publisher: Springer Science & Business Media
ISBN: 0817682260
Category : Mathematics
Languages : en
Pages : 283
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Book Description
This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
Author: Wen-Ching Winnie Li
Publisher: American Mathematical Soc.
ISBN: 1470449005
Category : Combinatorial number theory
Languages : en
Pages : 95
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Book Description
Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented. Research on zeta and L-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.
