Introduction to Arithmetic Geometry by Andrew V. Sutherland
Introduction to Arithmetic Geometry by Andrew V. Sutherland
Introduction to Arithmetic Geometry by Andrew V. Sutherland
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.
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.
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.