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.
This PDF Lectures covers the
following topics related to Arithmetic and Algebraic Geometry : Rings, Spectra,
Affine Varieties, Projective Varieties, Regularity, Curves.
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.
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.