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Książka Algebraic Geometry and Arithmetic Curves Erne Reine

Algebraic Geometry and Arithmetic Curves

Autor: Erne Reine, Qing Liu
Język: Angielski
Oprawa: Twarda
Wydawca: Oxford University Press
Dostępność: Dostępna u dostawcy
Wysyłamy za 10-18 dni
636.67 zł
This book is a general introduction to the theory of schemes, followed by applications to arithmetic...

Informacje o książce

Autor
Erne Reine, Qing Liu
Język
Angielski
Oprawa
Książka - Twarda
Data wydania
2002
strony
592
EAN
9780198502845
ISBN
0198502842
Enbook ID
04526810
Wydawca
Oxford University Press
Waga
1002
Wymiary
162 x 240 x 41

Pełny opis

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.

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