p adic Analysis in Arithmetic Geometry

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

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

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