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Arithmetic and Algebraic Geometry
This PDF Lectures covers the following topics related to Arithmetic and Algebraic Geometry : Rings, Spectra, Affine Varieties, Projective Varieties, Regularity, Curves.
Author(s): Shou-Wu Zhang
74 Pages
Arithmetic Geometry by Prof Szpiro
This PDF Lectures covers the following topics related to Arithmetic Geometry : Operations with modules, Schemes and projective schemes, Rings of dimension one, The compactified Picard group of an order of a number field, Different, discriminant and conductor, The classic theorems of the algebraic number theory, Heights of rational points on a scheme over a number field.
Author(s): Prof Szpiro
87 Pages
Introduction to Arithmetic Geometry by Andrew V. Sutherland
This note explains the following topics: Diophantine equations , Algebraic curves, The projective plane , Genus, Birational equivalence, The elliptic curve group law , Rational points on elliptic curves, The Sato-Tate conjecture, The Birch and Swinnerton-Dyer conjecture, Fermat’s Last Theorem, Jacobians of curves.
Author(s): Andrew V. Sutherland
36 Pages
Introduction to Arithmetic Geometry
Major topics topics coverd are: Absolute values on fields, Ostrowski's classification of absolute values on U, Cauchy sequences and completion, Inverse limits,Properties of Zp, The field of P -Adic numbers, P-adic expansions, Hensel's lemma, Finite fields, Profinite groups, Affine varieties, Morphisms and rational maps, Quadratic forms, Rational points on conics and Valuations on the function field of a curve.
Author(s): Bjorn Poonen
70 PagesAdvertisement
