algebraic geometry and arithmetic curves oxford graduate texts in mathematics

Download Book Algebraic Geometry And Arithmetic Curves Oxford Graduate Texts In Mathematics in PDF format. You can Read Online Algebraic Geometry And Arithmetic Curves Oxford Graduate Texts In Mathematics here in PDF, EPUB, Mobi or Docx formats.

Algebraic Geometry And Arithmetic Curves

Author : Qing Liu
ISBN : 9780191547805
Genre : Mathematics
File Size : 89. 48 MB
Format : PDF, ePub, Mobi
Download : 311
Read : 1129

Get This Book


This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

Algebraic Geometry And Arithmetic Curves

Author : Qing Liu
ISBN : 9780198502845
Genre : Mathematics
File Size : 51. 4 MB
Format : PDF, ePub
Download : 977
Read : 1214

Get This Book


'Will be useful to graduate students as an introduction to arithmetic algebraic geometry, and to more advanced readers and experts in the field.' -EMS'This book is unique in the current literature on algebraic and arithmetic geography, therefore a highly welcome addition to it, and particularly suitable for readers who want to approach more specialized works in this field with more ease. The exposition is exceptionally lucid, rigourous, coherent and comprehensive.' -Zentralblatt MATH'A thorough and far-reaching introduction to algebraic geometry in its scheme-theoretic setting... The rich bibliography with nearly 100 references enhances the value of this textbook as a great introduction and source for research.' -Zentralblatt MATHBased on the author's course for first-year graduate students this well-written text explains how the tools of algebraic geometry and of number theory can be applied to a study of curves. The book starts by introducing the essential background material and includes 600 exercises.

Algebraic Geometry And Arithmetic Curves

Author : Qing Liu
ISBN : 0199202494
Genre : Mathematics
File Size : 58. 73 MB
Format : PDF, Mobi
Download : 526
Read : 252

Get This Book


This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field.Singular curves are treated through a detailed study of the Picard group.The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford.This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students.

Fundamental Algebraic Geometry

Author : Barbara Fantechi
ISBN : 9780821842454
Genre : Mathematics
File Size : 69. 39 MB
Format : PDF, Kindle
Download : 572
Read : 876

Get This Book


Alexander Grothendieck introduced many concepts into algebraic geometry; they turned out to be astoundingly powerful and productive and truly revolutionized the subject. Grothendieck sketched his new theories in a series of talks at the Seminaire Bourbaki between 1957 and 1962 and collected his write-ups in a volume entitled ``Fondements de la Geometrie Algebrique,'' known as FGA. Much of FGA is now common knowledge; however, some of FGA is less well known, and its full scope is familiar to few. The present book resulted from the 2003 ``Advanced School in Basic Algebraic Geometry'' at the ICTP in Trieste, Italy. The book aims to fill in Grothendieck's brief sketches. There are four themes: descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. Most results are proved in full detail; furthermore, newer ideas are introduced to promote understanding, and many connections are drawn to newer developments. The main prerequisite is a thorough acquaintance with basic scheme theory. Thus this book is a valuable resource for anyone doing algebraic geometry.

Algebraic Geometry

Author : Ulrich Görtz
ISBN : 3834897221
Genre : Mathematics
File Size : 25. 1 MB
Format : PDF, Kindle
Download : 210
Read : 826

Get This Book


This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Rational Points On Varieties

Author : Bjorn Poonen
ISBN : 9781470437732
Genre : Algebraic varieties
File Size : 89. 24 MB
Format : PDF
Download : 428
Read : 967

Get This Book


This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.

Algebraic Geometry

Author : Robin Hartshorne
ISBN : 0387902449
Genre : Mathematics
File Size : 65. 94 MB
Format : PDF, ePub
Download : 754
Read : 602

Get This Book


This book provides an introduction to abstract algebraic geometry. It includes more than 400 exercises that offer specific examples as well as more specialized topics. From the reviews: "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions." --MATHEMATICAL REVIEWS

Riemann Surfaces

Author : Simon Donaldson
ISBN : 9780198526391
Genre : Mathematics
File Size : 68. 83 MB
Format : PDF, ePub, Mobi
Download : 536
Read : 396

Get This Book


An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

Algebraic Varieties

Author : G. Kempf
ISBN : 0521426138
Genre : Mathematics
File Size : 30. 16 MB
Format : PDF, Kindle
Download : 734
Read : 504

Get This Book


An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

Arithmetic Of L Functions

Author : Cristian Popescu
ISBN : 9780821886984
Genre : Mathematics
File Size : 29. 69 MB
Format : PDF, ePub, Docs
Download : 505
Read : 436

Get This Book



Top Download:

Best Books