An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces

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An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces

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Author : Wayne Aitken
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces written by Wayne Aitken 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 1996 with Mathematics categories.

The following gives a development of Arakelov theory general enough to handle not only regular arithmetic surfaces but also a large class of arithmetic surfaces whose generic fiber has singularities. This development culminates in an arithmetic Riemann-Roch theorem for such arithmetic surfaces. The first part of the memoir gives a treatment of Deligne's functorial intersection theory, and the second develops a class of intersection functions for singular curves which behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves.

Arakelov Geometry And Diophantine Applications

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Author : Emmanuel Peyre
language : en
Publisher: Springer Nature
Release Date : 2021-03-10

Arakelov Geometry And Diophantine Applications written by Emmanuel Peyre and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.

Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.

Hodge Theory In The Sobolev Topology For The De Rham Complex

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Author : Luigi Fontana
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Hodge Theory In The Sobolev Topology For The De Rham Complex written by Luigi Fontana 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 1998 with Mathematics categories.

In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.

Integrable Systems And Riemann Surfaces Of Infinite Genus

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Author : Martin Ulrich Schmidt
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Integrable Systems And Riemann Surfaces Of Infinite Genus written by Martin Ulrich Schmidt 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 1996 with Mathematics categories.

This memoir develops the spectral theory of the Lax operators of nonlinear Schrödinger-like partial differential equations with periodic boundary conditions. Their special curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus. The points corresponding to infinite energy are added. The resulting spaces are no longer Riemann surfaces in the usual sense, but they are quite similar to compact Riemann surfaces.

Model Theory And Linear Extreme Points In The Numerical Radius Unit Ball

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Author : Michael A. Dritschel
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Model Theory And Linear Extreme Points In The Numerical Radius Unit Ball written by Michael A. Dritschel 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 1997 with Mathematics categories.

This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.

The Classification Of Countable Homogeneous Directed Graphs And Countable Homogeneous N Tournaments

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Author : Gregory L. Cherlin
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

The Classification Of Countable Homogeneous Directed Graphs And Countable Homogeneous N Tournaments written by Gregory L. Cherlin 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 1998 with Mathematics categories.

In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.

Some Connections Between Isoperimetric And Sobolev Type Inequalities

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Author : Serguei Germanovich Bobkov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Some Connections Between Isoperimetric And Sobolev Type Inequalities written by Serguei Germanovich Bobkov 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 1997 with Art categories.

For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.

The Finite Irreducible Linear 2 Groups Of Degree 4

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Author : Dane Laurence Flannery
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

The Finite Irreducible Linear 2 Groups Of Degree 4 written by Dane Laurence Flannery 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 1997 with Mathematics categories.

This memoir contains a complete classification of the finite irreducible 2-subgroups of GL(4, C). Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by generating a set of monomial matrices. The problem is treated by a variety of techniques, including: elementary character theory; a method for describing Hasse diagrams of submodule lattices; and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups and Schur indices of their defining characters are also considered

Two Classes Of Riemannian Manifolds Whose Geodesic Flows Are Integrable

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Author : Kazuyoshi Kiyohara
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Two Classes Of Riemannian Manifolds Whose Geodesic Flows Are Integrable written by Kazuyoshi Kiyohara 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 1997 with Mathematics categories.

Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.

Gauge Theory On Compact Surfaces

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Author : Ambar Sengupta
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Gauge Theory On Compact Surfaces written by Ambar Sengupta 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 1997 with Mathematics categories.

In this paper we develop a concrete description of connections on principal bundles, possibly non-trivial, over compact surfaces and use this description to construct the Yang-Mills measure which underlies the Euclidean quantum theory of gauge fields, involving compact gauge groups, on compact connected two-dimensional Riemannian manifolds (possibly with boundary). Using this measure we compute expectation values of important random variables, the Wilson loops variables, corresponding to a broad class of configurations of loops on the surface.