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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 
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
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
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