Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
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 
p adic Analysis in Arithmetic Geometry
This note covers introduction, p adic numbers, Newton polygons, Multiplicative seminorms and berkovich space, The berkovich affine and projective line, Analytic spaces and function, Berkovich spaces of curves and integration.
Author(s): Michael Stoll
52 Pages
Investigations in Two Dimensional Arithmetic Geometry
This note covers the following topics: Integration on valuation fields over local fields, Integration on product spaces and GLn of a valuation field over a local field, Fubinis theorem and non linear changes of variables over a two dimensional local field, Two dimensional integration la Hrushovski Kazhdan, Ramification, Fubinis theorem and Riemann Hurwitz formulae and an explicit approach to residues on and canonical sheaves of arithmetic surfaces.
Author(s): Matthew Morrow
182 Pages
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.
Author(s): Stephen S. Kudla
56 Pages
Arithmetic Geometry Lecture Notes
This lecture note explains everything about Arithmetic Geometry.
Author(s): Arizona University
NA Pages