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

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9780199202492: Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

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.

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About the Author:

Qing Liu is Charge de recherche, Centre National de la Recherche Scientifique (CNRS) Laboratoire de Theorie des Nombres et d'Algorithmique Arithmetique, Universite Bordeaux 1.

Review:


"Although other books do offer a fast passage to modern number theory, ... only Liu provides a systematic development of algebraic geometry aimed at arithmetic."--Choice


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Qing Liu
Editorial: Oxford University Press, United Kingdom (2006)
ISBN 10: 0199202494 ISBN 13: 9780199202492
Nuevos Paperback Cantidad: 1
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The Book Depository
(London, Reino Unido)
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Descripción Oxford University Press, United Kingdom, 2006. Paperback. Estado de conservación: New. Language: English . Brand New 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. Nº de ref. de la librería AAZ9780199202492

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Qing Liu
Editorial: Oxford University Press, United Kingdom (2006)
ISBN 10: 0199202494 ISBN 13: 9780199202492
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Descripción Oxford University Press, United Kingdom, 2006. Paperback. Estado de conservación: New. Language: English . Brand New 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. Nº de ref. de la librería AAZ9780199202492

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Qing Liu (author), Reinie Erne (translator)
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ISBN 10: 0199202494 ISBN 13: 9780199202492
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Descripción OUP Oxford 2006-06-29, Oxford, 2006. paperback. Estado de conservación: New. Nº de ref. de la librería 9780199202492

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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97801992024920000000

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Descripción OUP Oxford, 2006. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería FU-9780199202492

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Descripción Oxford University Press. Paperback. Estado de conservación: new. BRAND NEW, Algebraic Geometry and Arithmetic Curves, Qing Liu, Reinie Erne, 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. Nº de ref. de la librería B9780199202492

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Descripción Estado de conservación: New. Bookseller Inventory # ST0199202494. Nº de ref. de la librería ST0199202494

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Descripción Oxford University Press, 2006. Estado de conservación: New. 2006. Paperback. 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. Translator(s): Erne, Reinie. Series: Oxford Graduate Texts in Mathematics. Num Pages: 600 pages, illustrations. BIC Classification: PBH; PBMW. Category: (P) Professional & Vocational. Dimension: 234 x 158 x 32. Weight in Grams: 872. . . . . . . Nº de ref. de la librería V9780199202492

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Liu, Qing
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Descripción Oxford University Press. Estado de conservación: New. 2006. Paperback. 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. Translator(s): Erne, Reinie. Series: Oxford Graduate Texts in Mathematics. Num Pages: 600 pages, illustrations. BIC Classification: PBH; PBMW. Category: (P) Professional & Vocational. Dimension: 234 x 158 x 32. Weight in Grams: 872. . . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780199202492

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Descripción Oxford University Press. Estado de conservación: New. Brand New. Nº de ref. de la librería 0199202494

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