Algebraic Geometry and Arithmetic Curves Oxford Graduate Texts in Mathematics 0199619476 Book 6 Qing Liu Reinie Erne PDF-Viewer TOH

Algebraic Geometry and Arithmetic Curves Oxford Graduate Texts in Mathematics 0199619476 Book 6 Qing Liu Reinie Erne PDF QYG

Algebraic Geometry and Arithmetic Curves Oxford Graduate Texts in Mathematics 0199619476 Book 6 Qing Liu Reinie Erne PDF Algebraic%20Geometry%20and%20Arithmetic%20Curves%20Oxford%20Graduate%20Texts%20in%20Mathematics%200199619476%20Book%206%20Qing%20Liu%20Reinie%20Erne

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PDF Algebraic Geometry and Arithmetic Curves Oxford Graduate Texts in Mathematics 0199619476 Book 6 Qing Liu Reinie Erne QYG

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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.
ebook,Qing Liu, Reinie Erne,Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics (0-19-961947-6) Book 6),Oxford University Press,Algebraic geometry,Geometry - Algebraic,Great Britain/British Isles,MATHEMATICS / Arithmetic,MATHEMATICS / Geometry / Algebraic,MATHEMATICS / Number Theory,Mathematics,Non-Fiction,Number theory,Pure mathematics,Scholarly/Undergraduate,Science/Math,Science/Mathematics,UNIVERSITY PRESS,Geometry - Algebraic,Mathematics / Arithmetic,Mathematics / Geometry / Algebraic,Mathematics / Number Theory,Mathematics,Science/Mathematics,Algebraic geometry,Number theory

Algebraic Geometry and Arithmetic Curves Oxford Graduate Texts in Mathematics 0199619476 Book 6 Qing Liu Reinie Erne Reviews :

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.

ebook,Qing Liu, Reinie Erne,Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics (0-19-961947-6) Book 6),Oxford University Press,Algebraic geometry,Geometry - Algebraic,Great Britain/British Isles,MATHEMATICS / Arithmetic,MATHEMATICS / Geometry / Algebraic,MATHEMATICS / Number Theory,Mathematics,Non-Fiction,Number theory,Pure mathematics,Scholarly/Undergraduate,Science/Math,Science/Mathematics,UNIVERSITY PRESS,Geometry - Algebraic,Mathematics / Arithmetic,Mathematics / Geometry / Algebraic,Mathematics / Number Theory,Mathematics,Science/Mathematics,Algebraic geometry,Number theory

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Product details File Size 72211 KB Print Length 577 pages Publisher Oxford University Press (June 29, 2006) Publication Date June 29, 2006 Sold by  Services LLC Language English ASIN B00O148F08

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