Algebraic Geometry and Arithmetic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry and Arithmetic Curves write by Qing Liu. This book was released on 2006-06-29. Algebraic Geometry and Arithmetic Curves available in PDF, EPUB and Kindle. 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.
Algebraic Geometry and Arithmetic Curves
Algebraic Geometry and Arithmetic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry and Arithmetic Curves write by 刘擎. This book was released on 2002. Algebraic Geometry and Arithmetic Curves available in PDF, EPUB and Kindle. Based on the author's course for first-year students this well-written 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.
Algebraic Geometry and Arithmetic Curves
Algebraic Geometry and Arithmetic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry and Arithmetic Curves write by Qing Liu. This book was released on 2006-06-29. Algebraic Geometry and Arithmetic Curves available in PDF, EPUB and Kindle. This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with 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 fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students.
Arithmetic of Algebraic Curves
Arithmetic of Algebraic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Arithmetic of Algebraic Curves write by Serguei A. Stepanov. This book was released on 1994-12-31. Arithmetic of Algebraic Curves available in PDF, EPUB and Kindle. Author S.A. Stepanov thoroughly investigates the current state of the theory of Diophantine equations and its related methods. Discussions focus on arithmetic, algebraic-geometric, and logical aspects of the problem. Designed for students as well as researchers, the book includes over 250 excercises accompanied by hints, instructions, and references. Written in a clear manner, this text does not require readers to have special knowledge of modern methods of algebraic geometry.
Algebraic Geometry
Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry write by Solomon Lefschetz. This book was released on 2012-09-05. Algebraic Geometry available in PDF, EPUB and Kindle. An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
