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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
Arithmetic and Algebraic Geometry
This PDF Lectures covers the following topics related to Arithmetic and Algebraic Geometry : Rings, Spectra, Affine Varieties, Projective Varieties, Regularity, Curves.
Author(s): Shou-Wu Zhang
74 Pages
Arithmetic Geometry by Prof Szpiro
This PDF Lectures covers the following topics related to Arithmetic Geometry : Operations with modules, Schemes and projective schemes, Rings of dimension one, The compactified Picard group of an order of a number field, Different, discriminant and conductor, The classic theorems of the algebraic number theory, Heights of rational points on a scheme over a number field.
Author(s): Prof Szpiro
87 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