Orientation Theory in Arithmetic Geometry

Overview & Synopsis

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 and nbsp,Etale cohomology.