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 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.
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.
Diophantine Equations
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Author :
language : en
Publisher: Academic Press
Release Date : 1969
Diophantine Equations written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Diophantine Equations
Notes On Geometry And Arithmetic
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Author : Daniel Coray
language : en
Publisher: Springer Nature
Release Date : 2020-07-06
Notes On Geometry And Arithmetic written by Daniel Coray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-06 with Mathematics categories.
This English translation of Daniel Coray’s original French textbook Notes de géométrie et d’arithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the most essential ideas from algebraic geometry and commutative algebra. Readers are invited to discover rational points on varieties through an appealing ‘hands on’ approach that offers a pathway toward active research in arithmetic geometry. Along the way, the reader encounters the state of the art on solving certain classes of polynomial equations with beautiful geometric realizations, and travels a unique ascent towards variations on the Hasse Principle. Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert’s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.
Rational Points On Smooth Cubic Hypersurfaces
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Author : Stafanos Papanikolopoulos
language : en
Publisher:
Release Date : 2014
Rational Points On Smooth Cubic Hypersurfaces written by Stafanos Papanikolopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Brauer Groups Tamagawa Measures And Rational Points On Algebraic Varieties
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Author : Jorg Jahnel
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-02
Brauer Groups Tamagawa Measures And Rational Points On Algebraic Varieties written by Jorg Jahnel 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 2014-12-02 with Mathematics categories.
The central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate type--both in terms of when such points exist and, if they do, their quantitative density. The book consists of three parts. In the first part, the author discusses the concept of a height and formulates Manin's conjecture on the asymptotics of rational points on Fano varieties. The second part introduces the various versions of the Brauer group. The author explains why a Brauer class may serve as an obstruction to weak approximation or even to the Hasse principle. This part includes two sections devoted to explicit computations of the Brauer-Manin obstruction for particular types of cubic surfaces. The final part describes numerical experiments related to the Manin conjecture that were carried out by the author together with Andreas-Stephan Elsenhans. The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties and will be a valuable reference for researchers and graduate students interested in that area.
Families Of Curves On Families Of Surfaces Degenerating To Normal Rational Cubic Surfaces In P Cubed
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Author : John Olaf Brevik
language : en
Publisher:
Release Date : 1996
Families Of Curves On Families Of Surfaces Degenerating To Normal Rational Cubic Surfaces In P Cubed written by John Olaf Brevik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.