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.
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.
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.
This PDF Lectures covers the
following topics related to Arithmetic and Algebraic Geometry : Rings, Spectra,
Affine Varieties, Projective Varieties, Regularity, Curves.
This note explains the following topics: Diophantine equations ,
Algebraic curves, The projective plane , Genus, Birational equivalence, The
elliptic curve group law , Rational points on elliptic curves, The Sato-Tate
conjecture, The Birch and Swinnerton-Dyer conjecture, Fermat’s Last Theorem,
Jacobians of curves.
The aim
of these notes is to describe some examples of modular forms whose Fourier
coefficients involve quantities from arithmetical algebraic geometry.
Major topics topics coverd are:
Absolute values on fields, Ostrowski's classification of absolute values on U,
Cauchy sequences and completion, Inverse limits,Properties of Zp, The field of P
-Adic numbers, P-adic expansions, Hensel's lemma, Finite fields, Profinite
groups, Affine varieties, Morphisms and rational maps, Quadratic forms, Rational
points on conics and Valuations on the function field of a curve.