Arithmetic and Algebraic Geometry

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

Arithmetic Geometry Lecture Notes

This lecture note explains everything about Arithmetic Geometry.

Author(s): Arizona University

NA Pages