ePub Cohomological Theory of Crystals over Function Fields (Ems Tracts in Mathematics) download

by Gebhard Bockle and Richard Pink

Author:

Gebhard Bockle and Richard Pink

ISBN13:

978-3037190746

ISBN:

3037190744

Language:

English

Publisher:

European Mathematical Society (October 15, 2009)

Category:

Science

Subcategory:

Mathematics

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1937 kb

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Gebhard Bockle and Richard Pink. Download all eBooks in PDF,ePub format for free. Reproduction of site books is authorized only for informative purposes and strictly for personal, private use.

Gebhard Bockle and Richard Pink. European Mathematical Society.

Bibliography, etc. Note: Includes bibliographical references (p. -179) and index. Personal Name: Pink, Richard. Corporate Name: European Mathematical Society.

There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental interactions of nature. In this article, several approaches are discussed, although the equations are in terms of electric and magnetic fields, potentials, and charges with currents, generally speaking. The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field.

Are you sure you want to remove Cohomological theory of crystals over function fields from your list? . Includes bibliographical references (p. EMS tracts in mathematics - 9, EMS tracts in mathematics - 9. Classifications.

Are you sure you want to remove Cohomological theory of crystals over function fields from your list? Cohomological theory of crystals over function fields. Published 2009 by European Mathematical Society in Zürich, Switzerland. Algebraic Geometry, Homology theory, Number theory. viii, 187 p. ; Number of pages.

EMS Tracts in Mathematics, 9. European Mathematical Society (EMS), Zu¨rich, 2009. viii+187 pp. ISBN 978-3-03719-074-6. Let k be a nite eld with q elements, and let A be a nitely generated Dedekind domain over k with A∗ nite. One main point of the book is the development of suitable derived categories of A-crystals and the construction of functors f ∗, ⊗L, and Rf! on these derived categories that behave analogously to the corresponding operations in -adic theory. Now the main reason for studying these τ -sheaves is that there are natural L-functions attached to them.

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Cohomological Theory of Crystals Over Function Fields (math) – G. Bockle".

This lecture series introduces in the first part a cohomological theory for . Advanced Courses in Mathematics - CRM Barcelona.

This lecture series introduces in the first part a cohomological theory for varieties in positive characteristic with finitely generated rings of this characteristic as coefficients developed jointly. Cite this chapter as: Böckle G. (2014) Cohomological Theory of Crystals over Function Fields and Applications. In: Bars . Longhi . Trihan F. (eds) Arithmetic Geometry over Global Function Fields.

Gebhard Bockle and Richard Pink - Cohomological Theory of Crystals over Function Fields (Ems Tracts in Mathematics). Gebhard Bockle and Richard Pink. Читать pdf. Georges De Menil, Richard Portes, Hans-Warner Sinn, Giuseppe Bertola, Philippe Martin, Jac Van Ours - Economic Policy 55 (No. 55). Georges De Menil, Richard Portes, Hans-Warner Sinn, Giuseppe Bertola, Philippe Martin, Jac Van Ours.

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 introduces $A$-crystals, which can be viewed as generalizations of families of $A$-motives, and studies their cohomology. While $A$-crystals are defined in terms of coherent sheaves together with a Frobenius map, in many ways they actually behave like constructible etale sheaves. A central result is a Lefschetz trace formula for $L$-functions of $A$-crystals, from which the rationality of these $L$-functions is immediate. Beyond its application to Goss's $L$-functions, the theory of $A$-crystals is closely related to the work of Emerton and Kisin on unit root $F$-crystals, and it is essential in an Eichler - Shimura type isomorphism for Drinfeld modular forms as constructed by the first author. The book is intended for researchers and advanced graduate students interested in the arithmetic of function fields and/or cohomology theories for varieties in positive characteristic. It assumes a good working knowledge in algebraic geometry as well as familiarity with homological algebra and derived categories, as provided by standard textbooks. Beyond that the presentation is largely self contained.

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