Erne Reinie (EN) — Algebraic Geometry and Arithmetic Curves

Тут можно читать онлайн книгу Erne Reinie (EN) - Algebraic Geometry and Arithmetic Curves - бесплатно полную версию (целиком). Жанр книги: Иностранная литература. Вы можете прочесть полную версию (весь текст) онлайн без регистрации и смс на сайте Lib-King.Ru (Либ-Кинг) или прочитать краткое содержание, аннотацию (предисловие), описание и ознакомиться с отзывами (комментариями) о произведении.

Algebraic Geometry and Arithmetic Curves
Язык книги: Английский
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Algebraic Geometry and Arithmetic Curves краткое содержание

Algebraic Geometry and Arithmetic Curves - описание и краткое содержание, автор Erne Reinie (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

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, Zariskis 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 Grothendiecks 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. Castelnuovos 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 - читать онлайн бесплатно полную версию (весь текст целиком)

Algebraic Geometry and Arithmetic Curves - читать книгу онлайн бесплатно, автор Erne Reinie (EN)

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