Algebraic Geometry and Arithmetic Curves - (Liu Qing)(Paperback)
Oxford University Press anglické Qing Liu 0199202494 Brožovaná
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, Zariskis Main Theorem). This is followed...
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, 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 desingularization (embedded or not) of
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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 desingularization (embedded or not) of
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