Cohomological Theory of Crystals over Function Fields

ISBN-10: 3037190744

ISBN-13: 9783037190746

Edition: 2009

Authors: Gebhard Bï¿½ckle, Richard Pink, European Mathematical Society Staff

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Description:

This book develops a new cohomological theory for schemes in positive characteristic $p$ and it applies this theory to give a purely algebraic proof of a conjecture of Goss on the rationality of certain $L$-functions arising in the arithmetic of function fields. These $L$-functions are power series over a certain ring $A$, associated to any family of Drinfeld $A$-modules or, more generally, of $A$-motives on a variety of finite type over the finite field $\mathbb{F}_p$. By analogy to the Weil conjecture, Goss conjectured that these $L$-functions are in fact rational functions. In 1996 Taguchi and Wan gave a first proof of Goss's conjecture by analytic methods a la Dwork. The present text…

Book details

List price: $64.00
Copyright year: 2009
Publisher: European Mathematical Society
Publication date: 10/15/2009
Binding: Hardcover
Pages: 195
Size: 7.00" wide x 9.50" long x 0.75" tall
Weight: 1.144
Language: English