Automorphic Forms And The Picard Number Of An Elliptic Surface

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Automorphic Forms And The Picard Number Of An Elliptic Surface

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Author : Peter F. Stiller
language : en
Publisher:
Release Date : 2014-01-15

Automorphic Forms And The Picard Number Of An Elliptic Surface written by Peter F. Stiller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Automorphic Forms And The Picard Number Of An Elliptic Surface

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Author : Peter F. Stiller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Automorphic Forms And The Picard Number Of An Elliptic Surface written by Peter F. Stiller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Technology & Engineering categories.

In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E,Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E,E) which is of I type (1,1), that is to say a class in H(E,9!) which can be viewed as a 2 subspace of H(E,E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p,p) is algebraic. In our case this is the Lefschetz Theorem on (I,l)-classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E,Z) for 2 its image under the natural mapping into H (E,t). Thus NS(E) modulo 2 torsion is Hl(E,n!) n H(E,Z) and th 1 b i f h -~ p measures e a ge ra c part 0 t e cohomology.

Automorphic Forms And The Picard Number Of An Elliptic Surface

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Author : Peter Stiller
language : en
Publisher: Springer Science & Business Media
Release Date : 1984

Automorphic Forms And The Picard Number Of An Elliptic Surface written by Peter Stiller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E,Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E,E) which is of I type (1,1), that is to say a class in H(E,9!) which can be viewed as a 2 subspace of H(E,E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p,p) is algebraic. In our case this is the Lefschetz Theorem on (I,l)-classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E,Z) for 2 its image under the natural mapping into H (E,t). Thus NS(E) modulo 2 torsion is Hl(E,n!) n H(E,Z) and th 1 b i f h -~ p measures e a ge ra c part 0 t e cohomology.

Special Values Of Dirichlet Series Monodromy And The Periods Of Automorphic Forms

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Author : Peter Stiller
language : en
Publisher: American Mathematical Soc.
Release Date : 1984

Special Values Of Dirichlet Series Monodromy And The Periods Of Automorphic Forms written by Peter Stiller and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

In this paper we explore a relationship that exists between the classical cusp form for subgroups of finite index in [italic]SL2([double-struck capital]Z) and certain differential equations, and we develop a connection between the equation's monodromy representation and the special values in the critical strip of the Dirichlet series associated to the cusp form.

P Adic Methods In Number Theory And Algebraic Geometry

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Author : Alan Adolphson
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

P Adic Methods In Number Theory And Algebraic Geometry written by Alan Adolphson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

Two meetings of the AMS in the autumn of 1989 - one at the Stevens Institute of Technology and the other at Ball State University - included Special Sessions on the role of p-adic methods in number theory and algebraic geometry. This volume grew out of these Special Sessions. Drawn from a wide area of mathematics, the articles presented here provide an excellent sampling of the broad range of trends and applications in p-adic methods.

Modular Forms And String Duality

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Author : Noriko Yui, Helena Verrill, and Charles F. Doran
language : en
Publisher: American Mathematical Soc.
Release Date :

Modular Forms And String Duality written by Noriko Yui, Helena Verrill, and Charles F. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

"This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.

Manifolds And Modular Forms

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Author : Friedrich Hirzebruch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Manifolds And Modular Forms written by Friedrich Hirzebruch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Technology & Engineering categories.

This book provides a comprehensive introduction to the theory of elliptic genera due to Ochanine, Landweber, Stong, and others. The theory describes a new cobordism invariant for manifolds in terms of modular forms. The book evolved from notes of a course given at the University of Bonn. After providing some background material elliptic genera are constructed, including the classical genera signature and the index of the Dirac operator as special cases. Various properties of elliptic genera are discussed, especially their behaviour in fibre bundles and rigidity for group actions. For stably almost complex manifolds the theory is extended to elliptic genera of higher level. The text is in most parts self-contained. The results are illustrated by explicit examples and by comparison with well-known theorems. The relevant aspects of the theory of modular forms are derived in a seperate appendix, providing also a useful reference for mathematicians working in this field.

Calabi Yau Varieties And Mirror Symmetry

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Author : Noriko Yui
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Calabi Yau Varieties And Mirror Symmetry written by Noriko Yui and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The idea of mirror symmetry originated in physics, but in recent years, the field of mirror symmetry has exploded onto the mathematical scene. It has inspired many new developments in algebraic and arithmetic geometry, toric geometry, the theory of Riemann surfaces, and infinite-dimensional Lie algebras among others. The developments in physics stimulated the interest of mathematicians in Calabi-Yau varieties. This led to the realization that the time is ripe for mathematicians, armed with many concrete examples and alerted by the mirror symmetry phenomenon, to focus on Calabi-Yau varieties and to test for these special varieties some of the great outstanding conjectures, e.g., the modularity conjecture for Calabi-Yau threefolds defined over the rationals, the Bloch-Beilinson conjectures, regulator maps of higher algebraic cycles, Picard-Fuchs differential equations, GKZ hypergeometric systems, and others. The articles in this volume report on current developments. The papers are divided roughly into two categories: geometric methods and arithmetic methods. One of the significant outcomes of the workshop is that we are finally beginning to understand the mirror symmetry phenomenon from the arithmetic point of view, namely, in terms of zeta-functions and L-series of mirror pairs of Calabi-Yau threefolds. The book is suitable for researchers interested in mirror symmetry and string theory.

Tale Cohomology Of Rigid Analytic Varieties And Adic Spaces

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Author : Roland Huber
language : en
Publisher: Springer
Release Date : 2013-07-01

Tale Cohomology Of Rigid Analytic Varieties And Adic Spaces written by Roland Huber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Mathematics categories.

The aim of this book is to give an introduction to adic spaces and to develop systematically their étale cohomology. First general properties of the étale topos of an adic space are studied, in particular the points and the constructible sheaves of this topos. After this the basic results on the étale cohomology of adic spaces are proved: base change theorems, finiteness, Poincaré duality, comparison theorems with the algebraic case.

Automorphic Forms Attached To Differential Equations And Relationships With The Picard Number Of An Elliptic Surface

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Author : Peter Stiller
language : en
Publisher:
Release Date : 1983

Automorphic Forms Attached To Differential Equations And Relationships With The Picard Number Of An Elliptic Surface written by Peter Stiller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Algebraic functions categories.