Algebraic Geometry and Arithmetic Curves

Author: Qing Liu

Publisher: Oxford University Press

ISBN:

Category: Mathematics

Page: 592

View: 818

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.

A New English and Dutch Dictionary;

Wherein the Inìtial Ènglish Words are Accènted, Accórding to the Dutch Pronunciátion ; and Âlso Expláined by Synònima's, and a Varíety of Phráses. To which are Added : Catalogues of the Chrìstian Námes, Both of Men and Wòmen ; and Âlso of the Chief Coùntries, Cities, Nátions, & C. of the World

Author: John Holtrop

Publisher:

ISBN:

Category: Dutch language

Page: 1022

View: 332

The English Student's Companion

A Dictionary of Verbs, Substantives and Adjectives with the Prepositions They Govern, According to the Authority of the Best English Classics; Principally Followed from Melford's Phraseological Dictionary

Author: Frederick Martin Cowan

Publisher:

ISBN:

Category:

Page: 308

View: 407

Volledige Leercursus Der Engelsche Taal

Uitbreiding van het geleerde ... de spraakkunst in haren geheelen omvang, uitzonderingen, nieuwe vormen en taalwendingen

Author: Johan Nicolaas Valkhoff

Publisher:

ISBN:

Category:

Page: 164

View: 662