This note explains the
following topics: Classical arithmetic geometry, The Convergence Theorem, The
link with the classical AGM sequence, Point counting on elliptic curves, A theta
structure induced by Frobenius.
This note covers
the following topics: Rational points on varieties, Heights, Arakelov Geometry,
Abelian Varieties, The Brauer-Manin Obstruction, Birational Geomery, Statistics
of Rational Points, Zeta functions.
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, Fermatís Last Theorem,
Jacobians of curves.
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.