Algebraic Geometry and Arithmetic Curves (Oxford Graduate by Qing Liu,Reinie Erne PDF

By Qing Liu,Reinie Erne

ISBN-10: 0198502842

ISBN-13: 9780198502845

ISBN-10: 0199202494

ISBN-13: 9780199202492

This booklet is a common creation to the idea of schemes, via functions to mathematics surfaces and to the idea of relief of algebraic curves.

The first half introduces easy items equivalent to schemes, morphisms, base swap, neighborhood houses (normality, regularity, Zariski's major Theorem). this can be by means of the extra worldwide element: coherent sheaves and a finiteness theorem for his or her cohomology teams. Then follows a bankruptcy on sheaves of differentials, dualizing sheaves, and Grothendieck's duality concept. the 1st half ends with the concept of Riemann-Roch and its program to the learn of gentle projective curves over a field.
Singular curves are taken care of via an in depth learn of the Picard group.

The moment half starts off with blowing-ups and desingularisation (embedded or no longer) of fibered surfaces over a Dedekind ring that leads directly to intersection concept on mathematics surfaces. Castelnuovo's criterion is proved and likewise the life of the minimum standard version. This ends up in the research of aid of algebraic curves. The case of elliptic curves is studied intimately. The booklet concludes with the funadmental theorem of reliable relief of Deligne-Mumford.

The publication is basically self-contained, together with the required fabric on commutative algebra. the must haves are for that reason few, and the booklet may still swimsuit a graduate pupil. It includes many examples and approximately six hundred exercises.

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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics (0-19-961947-6)) by Qing Liu,Reinie Erne


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