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Algebraic Geometry and Arithmetic Curves
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Algebraic Geometry and Arithmetic Curves Paperback - 2006

by Qing Liu; Reinie Erne (Translator)

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From the publisher

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 desingularization (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.

First line

Unless otherwise specified, all rings in this book will be supposed commutative and with unit.

Details

  • Title Algebraic Geometry and Arithmetic Curves
  • Author Qing Liu; Reinie Erne (Translator)
  • Binding Paperback
  • Pages 600
  • Volumes 1
  • Language ENG
  • Publisher Oxford University Press (UK)
  • Publication date 2006-08-24
  • Illustrated Yes
  • Features Bibliography, Illustrated, Index, Table of Contents
  • ISBN 9780199202492 / 0199202494
  • Weight 1.97 lbs (0.89 kg)
  • Dimensions 9.18 x 6.16 x 1.27 in (23.32 x 15.65 x 3.23 cm)
  • Category Mathematics
  • Dewey Decimal Code 516.352

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Algebraic Geometry and Arithmetic Curves

Algebraic Geometry and Arithmetic Curves

by Qing Liu

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Paperback. New. New Book; Fast Shipping from UK; Not signed; Not First Edition; This new-in-paperback edition provides an 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. Clear
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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)
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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

by Liu, Qing

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Oxford University Press, 2006. *Price HAS BEEN REDUCED by 10% until Monday, June 8 (weekend SALE item)* 577 pp., paperback, 1 tiny blemish to fore edge else fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
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Algebraic Geometry and Arithmetic Curves

Algebraic Geometry and Arithmetic Curves

by Qing Liu

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Paperback / softback. New. This new-in-paperback edition provides an 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. Clear explanations of both theory and applications, and almost 600 exercises are included in the text.
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Algebraic Geometry and Arithmetic Curves

Algebraic Geometry and Arithmetic Curves

by Qing Liu

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9780199202492 / 0199202494
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Paperback / softback. New. This new-in-paperback edition provides an 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. Clear explanations of both theory and applications, and almost 600 exercises are included in the text.
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Algebraic Geometry and Arithmetic Curves
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Algebraic Geometry and Arithmetic Curves

by Liu, Qing,

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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)
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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)
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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics) (Oxford Graduate Texts in Mathematics, 6)

by Liu, Qing

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Algebraic Geometry and Arithmetic Curves
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Algebraic Geometry and Arithmetic Curves

by Liu, Qing,

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