Investigations in Two Dimensional 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

Orientation Theory in Arithmetic Geometry

This note explains the following topics : Notations and conventions, Absolute cohomology and purity, Functoriality instable homotopy, Absolute cohomology, Absolute purity, Analytical invariance, Orientation and characteristic classes, Orientation theory and Chern classes, Thom classes and MGL modules, Fundamental classes, Intersection theory, Gysin morphisms and localization long exact sequence, Residues and the case of closed immersions, Projective lci morphisms, Uniqueness, Riemann Roch formulas, Todd classes, The case of closed immersions, The general case, Principle of computation, Change of orientation, Universal formulas and the Chern character, Residues and symbols, Residual Riemann Roch formula The axiomatic of Panin revisited Axioms for arithmetic cohomologies and  Etale cohomology.

Author(s): Frederic Deglise

82 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