Counting Rational Points On Cubic Surfaces
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Counting Rational Points On Cubic Surfaces
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Author : Efthymios Sofos
language : en
Publisher:
Release Date : 2011
Counting Rational Points On Cubic Surfaces written by Efthymios Sofos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Rational points (Geometry) categories.
Counting Rational Points On Smooth Cubic Surfaces
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Author : Efthymios Sofos
language : en
Publisher:
Release Date : 2015
Counting Rational Points On Smooth Cubic Surfaces written by Efthymios Sofos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Rational Points On Cubic Surfaces
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Author : Niklas Broberg
language : en
Publisher:
Release Date : 1999
Rational Points On Cubic Surfaces written by Niklas Broberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Rational Points On The Exponent E6 Cubic Surface
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Author : Michael Joyce
language : en
Publisher:
Release Date : 2005
Rational Points On The Exponent E6 Cubic Surface written by Michael Joyce and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Surfaces, Cubic categories.
Rational Points On Algebraic Varieties
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Author : Emmanuel Peyre
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Rational Points On Algebraic Varieties written by Emmanuel Peyre and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.
Counting Rational Points On Curves And Surfaces
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Author : Niklas Broberg
language : en
Publisher:
Release Date : 2002
Counting Rational Points On Curves And Surfaces written by Niklas Broberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Torsors And Rational Points
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Author : Alexei Skorobogatov
language : en
Publisher: Cambridge University Press
Release Date : 2001-07-05
Torsors And Rational Points written by Alexei Skorobogatov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-05 with Mathematics categories.
This book, first published in 2001, is a complete and coherent exposition of the theory and applications of torsors to rational points.
Torsors Tale Homotopy And Applications To Rational Points
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Author : Alexei N. Skorobogatov
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-18
Torsors Tale Homotopy And Applications To Rational Points written by Alexei N. Skorobogatov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.
Point Counting And The Zilber Pink Conjecture
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Author : Jonathan Pila
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Point Counting And The Zilber Pink Conjecture written by Jonathan Pila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.
Number Theory
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Author : Takashi Aoki
language : en
Publisher: World Scientific
Release Date : 2010
Number Theory written by Takashi Aoki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory ? quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms ? Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al's paper gives a very thorough survey on functional relations of root system zeta-functions, Hoshi?Miyake's paper is a continuation of Miyake's long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia's paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura's paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers.Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students.