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Arithmetic Geometry Books

This section contains free e-books and guides on Arithmetic Geometry, some of the resources in this section can be viewed online and some of them can be downloaded.

A Generalized Arithmetic Geometric Mean

This note explains the following topics: Classical arithmetic geometry, The Convergence Theorem, The link with the classical AGM sequence, Point counting on elliptic curves, A theta structure induced by Frobenius.


s 95Pages

Algebraic and Arithmetic Geometry

This note covers the following topics: Rational points on varieties, Heights, Arakelov Geometry, Abelian Varieties, The Brauer-Manin Obstruction, Birational Geomery, Statistics of Rational Points, Zeta functions.


s 63Pages

Euler Systems and Arithmetic Geometry

This note explains the following topics: Galois Modules, Discrete Valuation Rings, The Galois Theory of Local Fields, Ramification Groups, Witt Vectors, Projective Limits of Groups of Units of Finite Fields, The Absolute Galois Group of a Local Field, Group Cohomology, Galois Cohomology, Abelian Varieties, Selmer Groups of Abelian Varieties, Kummer Theory, Torsors for Algebraic Groups, The Main Theorem, Operators on Modular Curves, Heegner Points, Hecke Operators on Heegner Points and Local Behavior of Cohomology Classes.


s 168Pages

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, Fermatís Last Theorem, Jacobians of curves.


s 36Pages

Modular forms and arithmetic geometry by Stephen S. Kudla

The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry.


s 56Pages

Arithmetic Geometry Lecture Notes

This lecture note explains everything about Arithmetic Geometry.


s NAPages

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.


s 70Pages