Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform - 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 Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform write by Reinhardt Kiehl. This book was released on 2013-03-14. Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform available in PDF, EPUB and Kindle. The authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.
Etale Cohomology and the Weil Conjecture
Etale Cohomology and the Weil Conjecture - 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 Etale Cohomology and the Weil Conjecture write by Eberhard Freitag. This book was released on 2013-03-14. Etale Cohomology and the Weil Conjecture available in PDF, EPUB and Kindle. Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne's proof of the Weil conjec tures. For the convenience of the speakers the present authors - who were also the organisers of that meeting - prepared short notes containing the central definitions and ideas of the proofs. The unexpected interest for these notes and the various suggestions to publish them encouraged us to work somewhat more on them and fill out the gaps. Our aim was to develop the theory in as self contained and as short a manner as possible. We intended especially to provide a complete introduction to etale and l-adic cohomology theory including the monodromy theory of Lefschetz pencils. Of course, all the central ideas are due to the people who created the theory, especially Grothendieck and Deligne. The main references are the SGA-notes [64-69]. With the kind permission of Professor J. A. Dieudonne we have included in the book that finally resulted his excellent notes on the history of the Weil conjectures, as a second introduction. Our original notes were written in German. However, we finally followed the recommendation made variously to publish the book in English. We had the good fortune that Professor W. Waterhouse and his wife Betty agreed to translate our manuscript. We want to thank them very warmly for their willing involvement in such a tedious task. We are very grateful to the staff of Springer-Verlag for their careful work.
Weil's Conjecture for Function Fields
Weil's Conjecture for Function Fields - 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 Weil's Conjecture for Function Fields write by Dennis Gaitsgory. This book was released on 2019-02-19. Weil's Conjecture for Function Fields available in PDF, EPUB and Kindle. A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil’s conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting l-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors. Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil’s conjecture. The proof of the product formula will appear in a sequel volume.
The Weil Conjectures
The Weil Conjectures - 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 Weil Conjectures write by Karen Olsson. This book was released on 2019-07-16. The Weil Conjectures available in PDF, EPUB and Kindle. A New York Times Editors' Pick and Paris Review Staff Pick "A wonderful book." --Patti Smith "I was riveted. Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge." --Parul Sehgal, The New York Times An eloquent blend of memoir and biography exploring the Weil siblings, math, and creative inspiration Karen Olsson’s stirring and unusual third book, The Weil Conjectures, tells the story of the brilliant Weil siblings—Simone, a philosopher, mystic, and social activist, and André, an influential mathematician—while also recalling the years Olsson spent studying math. As she delves into the lives of these two singular French thinkers, she grapples with their intellectual obsessions and rekindles one of her own. For Olsson, as a math major in college and a writer now, it’s the odd detours that lead to discovery, to moments of insight. Thus The Weil Conjectures—an elegant blend of biography and memoir and a meditation on the creative life. Personal, revealing, and approachable, The Weil Conjectures eloquently explores math as it relates to intellectual history, and shows how sometimes the most inexplicable pursuits turn out to be the most rewarding.
The Local Langlands Conjecture for GL(2)
The Local Langlands Conjecture for GL(2) - 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 Conjecture for GL(2) write by Colin J. Bushnell. This book was released on 2006-08-29. The Local Langlands Conjecture for GL(2) available in PDF, EPUB and Kindle. 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.
