Items related to Algebraic Geometry and Arithmetic Curves (Oxford Graduate...
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 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. 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.
"synopsis" may belong to another edition of this title.
About the Author:
"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
Qing Liu is at 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
"About this title" may belong to another edition of this title.
- PublisherOxford University Press
- Publication date2002
- ISBN 10 0198502842
- ISBN 13 9780198502845
- BindingHardcover
- Edition number1
- Number of pages592
- Rating
Buy New
Learn more about this copy
US$ 174.30
Shipping:
US$ 2.64
Within U.S.A.
Top Search Results from the AbeBooks Marketplace
Seller Image
Algebraic Geometry and Arithmetic Curves
Published by
Oxford University Press
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: 5
Seller:
Rating
Book Description Condition: New. Seller Inventory # 75730-n
Buy New
US$ 174.30
Convert currency
Stock Image
Algebraic Geometry and Arithmetic Curves 6 Oxford Graduate Texts in Mathematics 0199619476
Published by
Oxford University Press, USA
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: > 20
Seller:
Rating
Book Description HRD. Condition: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # L1-9780198502845
Buy New
US$ 176.95
Convert currency
Stock Image
Algebraic Geometry and Arithmetic Curves
Published by
OUP Oxford
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: > 20
Seller:
Rating
Book Description Condition: New. PRINT ON DEMAND Book; New; Fast Shipping from the UK. No. book. Seller Inventory # ria9780198502845_lsuk
Buy New
US$ 168.80
Convert currency
Stock Image
ALGEBRAIC GEOMETRY AND ARITHMETI
Published by
Oxford University Press
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: 1
Seller:
Rating
Book Description Condition: New. New. In shrink wrap. Looks like an interesting title! 2.28. Seller Inventory # Q-0198502842
Buy New
US$ 177.61
Convert currency
Seller Image
Algebraic Geometry and Arithmetic Curves
Published by
Oxford University Press
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: 5
Seller:
Rating
Book Description Condition: New. Seller Inventory # 75730-n
Buy New
US$ 168.79
Convert currency
Seller Image
Algebraic Geometry and Arithmetic Curves (Hardcover)
Published by
Oxford University Press, Oxford
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: 1
Seller:
Rating
Book Description Hardcover. Condition: new. Hardcover. 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 chapteron 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 overa 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 concludeswith the funadmental theorem of stable reduction of Deligne-Mumford.The book is essentially self-contained, including the necessary material on commutative algebra. Theprerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises. Based on the author's course for first-year graduate students this 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9780198502845
Buy New
US$ 156.90
Convert currency
Stock Image
Algebraic Geometry and Arithmetic Curves 6 Oxford Graduate Texts in Mathematics 0199619476
Published by
Oxford University Press, USA
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: > 20
Seller:
Rating
Book Description HRD. Condition: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # L1-9780198502845
Buy New
US$ 171.75
Convert currency
Stock Image
Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)
Published by
Oxford University Press
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: > 20
Seller:
Rating
Book Description Condition: New. Seller Inventory # ABLIING23Feb2215580042582
Buy New
US$ 205.16
Convert currency
Stock Image
Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)
Published by
Oxford University Press
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: > 20
Seller:
Rating
Book Description Condition: New. Seller Inventory # I-9780198502845
Buy New
US$ 241.00
Convert currency
Seller Image
Algebraic Geometry and Arithmetic Curves (Hardcover)
Published by
Oxford University Press, Oxford
(2002)
ISBN 10: 0198502842
ISBN 13: 9780198502845
New
Hardcover
Quantity: 1
Seller:
Rating
Book Description Hardcover. Condition: new. Hardcover. 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 chapteron 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 overa 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 concludeswith the funadmental theorem of stable reduction of Deligne-Mumford.The book is essentially self-contained, including the necessary material on commutative algebra. Theprerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises. Based on the author's course for first-year graduate students this 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780198502845
Buy New
US$ 244.30
Convert currency