Graduated School Arithmetic ...
Author : Benjamin Templar
Publisher :
Page : 154 pages
File Size : 32,18 MB
Release : 1872
Category : Arithmetic
ISBN :
Author : Benjamin Templar
Publisher :
Page : 154 pages
File Size : 32,18 MB
Release : 1872
Category : Arithmetic
ISBN :
Author : Benjamin TEMPLAR
Publisher :
Page : 28 pages
File Size : 29,95 MB
Release : 1876
Category :
ISBN :
Author : Thomas A. Garrity
Publisher : 清华大学出版社有限公司
Page : 380 pages
File Size : 23,64 MB
Release : 2004
Category : Mathematics
ISBN : 9787302090854
Author : Dennis Heywood
Publisher :
Page : 42 pages
File Size : 40,66 MB
Release : 1883
Category : Arithmetic
ISBN :
Author : Nelson Thomas and sons, ltd
Publisher :
Page : 110 pages
File Size : 14,82 MB
Release : 1880
Category :
ISBN :
Author : Qing Liu
Publisher : Oxford University Press
Page : 593 pages
File Size : 34,20 MB
Release : 2006-06-29
Category : Mathematics
ISBN : 0191547808
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.
Author : Serge Lang
Publisher :
Page : 475 pages
File Size : 39,3 MB
Release : 1988-01
Category : Mathematics
ISBN : 9783540967873
Author : W J. Dickinson
Publisher :
Page : 44 pages
File Size : 33,79 MB
Release : 1879
Category : Geometry
ISBN :
Author : W J. Dickinson
Publisher :
Page : 96 pages
File Size : 47,75 MB
Release : 1879
Category :
ISBN :
Author : Catalogues
Publisher :
Page : 200 pages
File Size : 16,36 MB
Release : 1876
Category :
ISBN :