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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.

Arithmetic Geometry Books
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A Generalized Arithmetic Geometric Mean

PDF | 95 Pages | English
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.

 
Algebraic and Arithmetic Geometry

PDF | 63 Pages | English
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.

 
Euler Systems and Arithmetic Geometry

PDF | 168 Pages | English
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.

 
Study Group on Arithmetic Geometry

Online | NA Pages | English
This is a website for the study group on Arithmetic Geomtery, here are some material for this study group. Topics covered includes: Coordinate modules, Rapoport-Zink spaces by Scholze-Weinstein, p-adic Hodge theory by Scholze, p-divisible groups with CM, Artin's approximation, Ihara-Langlands-Kottwitz method, Global Langlands, De Rham cohomology and Gauss-Manin connections, Integral models of Shimura varieties, Perfectoid spaces, p-divisible groups and displays, Drinfeld upper half spaces, etale cohomology, p-adic Hodge theory, crystalline cohomology, Beilinson's work.

 
Introduction to Arithmetic Geometry by Andrew V. Sutherland

PDF | 36 Pages | English
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.

 
Modular forms and arithmetic geometry by Stephen S. Kudla

PDF | 56 Pages | English
The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry.

 
Arithmetic Geometry Lecture Notes

Online | NA Pages | English
This lecture note explains everything about Arithmetic Geometry.

 
Introduction to Arithmetic Geometry

PDF | 70 Pages | English
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.

 
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