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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.
Author(s): Robert Carls
95Pages
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.
Author(s): Caucher Birkar and Tony Feng
63Pages
This note explains the following topics: Galois Modules, Discrete Valuation Rings, The Galois Theory of Local Fields, Ramification Groups, Witt Vectors, Projective Limits of Groups of Units of Finite Fields, The Absolute Galois Group of a Local Field, Group Cohomology, Galois Cohomology, Abelian Varieties, Selmer Groups of Abelian Varieties, Kummer Theory, Torsors for Algebraic Groups, The Main Theorem, Operators on Modular Curves, Heegner Points, Hecke Operators on Heegner Points and Local Behavior of Cohomology Classes.
Author(s): Barry Mazur and Tom Weston
168Pages
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.
Author(s): Andrew V. Sutherland
36Pages
The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry.
Author(s): Stephen S. Kudla
56Pages
This lecture note explains everything about Arithmetic Geometry.
Author(s): Arizona University
NAPages
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.
Author(s): Bjorn Poonen
70Pages
