

This section contains free ebooks and guides on Arithmetic Geometry, some of the resources in this section can be viewed online and some of them can be downloaded.




A Generalized Arithmetic Geometric MeanRobert CarlsPDF  95 Pages  EnglishThis 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.
 Algebraic and Arithmetic GeometryCaucher Birkar and Tony FengPDF  63 Pages  EnglishThis note covers
the following topics: Rational points on varieties, Heights, Arakelov Geometry,
Abelian Varieties, The BrauerManin Obstruction, Birational Geomery, Statistics
of Rational Points, Zeta functions.
 Euler Systems and Arithmetic GeometryBarry Mazur and Tom WestonPDF  168 Pages  EnglishThis
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.
 Study Group on Arithmetic GeometryTeruyoshi YoshidaOnline  NA Pages  EnglishThis is a website for the study group
on Arithmetic Geomtery, here are some material for this study group. Topics
covered includes: Coordinate modules, RapoportZink spaces by ScholzeWeinstein,
padic Hodge theory by Scholze, pdivisible groups with CM, Artin's
approximation, IharaLanglandsKottwitz method, Global Langlands, De Rham
cohomology and GaussManin connections, Integral models of Shimura varieties,
Perfectoid spaces, pdivisible groups and displays, Drinfeld upper half spaces,
etale cohomology, padic Hodge theory, crystalline cohomology, Beilinson's
work.
 Introduction to Arithmetic Geometry by Andrew V. SutherlandAndrew V.
SutherlandPDF  36 Pages  EnglishThis 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 SatoTate
conjecture, The Birch and SwinnertonDyer conjecture, Fermat’s Last Theorem,
Jacobians of curves.
   Introduction to Arithmetic GeometryBjorn PoonenPDF  70 Pages  EnglishMajor 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, Padic 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.









