To an Effective Local Langlands Correspondence - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook To an Effective Local Langlands Correspondence write by Colin J. Bushnell. This book was released on 2014-08-12. To an Effective Local Langlands Correspondence available in PDF, EPUB and Kindle. Let F be a non-Archimedean local field. Let \mathcal{W}_{F} be the Weil group of F and \mathcal{P}_{F} the wild inertia subgroup of \mathcal{W}_{F}. Let \widehat {\mathcal{W}}_{F} be the set of equivalence classes of irreducible smooth representations of \mathcal{W}_{F}. Let \mathcal{A}^{0}_{n}(F) denote the set of equivalence classes of irreducible cuspidal representations of \mathrm{GL}_{n}(F) and set \widehat {\mathrm{GL}}_{F} = \bigcup _{n\ge 1} \mathcal{A}^{0}_{n}(F). If \sigma \in \widehat {\mathcal{W}}_{F}, let ^{L}{\sigma }\in \widehat {\mathrm{GL}}_{F} be the cuspidal representation matched with \sigma by the Langlands Correspondence. If \sigma is totally wildly ramified, in that its restriction to \mathcal{P}_{F} is irreducible, the authors treat ^{L}{\sigma} as known. From that starting point, the authors construct an explicit bijection \mathbb{N}:\widehat {\mathcal{W}}_{F} \to \widehat {\mathrm{GL}}_{F}, sending \sigma to ^{N}{\sigma}. The authors compare this "naïve correspondence" with the Langlands correspondence and so achieve an effective description of the latter, modulo the totally wildly ramified case. A key tool is a novel operation of "internal twisting" of a suitable representation \pi (of \mathcal{W}_{F} or \mathrm{GL}_{n}(F)) by tame characters of a tamely ramified field extension of F, canonically associated to \pi. The authors show this operation is preserved by the Langlands correspondence.
Langlands Correspondence for Loop Groups
Langlands Correspondence for Loop Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Langlands Correspondence for Loop Groups write by Edward Frenkel. This book was released on 2007-06-28. Langlands Correspondence for Loop Groups available in PDF, EPUB and Kindle. The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Automorphic Forms and Galois Representations: Volume 1
Automorphic Forms and Galois Representations: Volume 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Automorphic Forms and Galois Representations: Volume 1 write by Fred Diamond. This book was released on 2014-10-16. Automorphic Forms and Galois Representations: Volume 1 available in PDF, EPUB and Kindle. Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.
The Local Langlands Correspondence in Singular Families of Representations
The Local Langlands Correspondence in Singular Families of Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Local Langlands Correspondence in Singular Families of Representations write by Tibor András Backhausz. This book was released on 2022. The Local Langlands Correspondence in Singular Families of Representations available in PDF, EPUB and Kindle.
Automorphic Forms and Galois Representations
Automorphic Forms and Galois Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Automorphic Forms and Galois Representations write by Fred Diamond. This book was released on 2014-10-16. Automorphic Forms and Galois Representations available in PDF, EPUB and Kindle. Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
