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Arithmetic Geometry Books

There are many online resources where you can find free Arithmetic Geometry books to download in PDF format, including online textbooks, ebooks, lecture notes, and more, covering basic, beginner, and advanced concepts for those looking for an introduction to the subject or a deeper understanding of it.

Investigations in Two Dimensional Arithmetic Geometry

This note covers the following topics: Integration on valuation fields over local fields, Integration on product spaces and GLn of a valuation field over a local field, Fubinis theorem and non linear changes of variables over a two dimensional local field, Two dimensional integration la Hrushovski Kazhdan, Ramification, Fubinis theorem and Riemann Hurwitz formulae and an explicit approach to residues on and canonical sheaves of arithmetic surfaces.


s 182Pages

Orientation Theory in Arithmetic Geometry

This note explains the following topics : Notations and conventions, Absolute cohomology and purity, Functoriality instable homotopy, Absolute cohomology, Absolute purity, Analytical invariance, Orientation and characteristic classes, Orientation theory and Chern classes, Thom classes and MGL modules, Fundamental classes, Intersection theory, Gysin morphisms and localization long exact sequence, Residues and the case of closed immersions, Projective lci morphisms, Uniqueness, Riemann Roch formulas, Todd classes, The case of closed immersions, The general case, Principle of computation, Change of orientation, Universal formulas and the Chern character, Residues and symbols, Residual Riemann Roch formula The axiomatic of Panin revisited Axioms for arithmetic cohomologies and  Etale cohomology.


s 82Pages

Arithmetic and Algebraic Geometry

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


s 74Pages

Arithmetic Geometry by Prof Szpiro

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.


s 87Pages

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, Fermatís Last Theorem, Jacobians of curves.


s 36Pages

Modular forms and arithmetic geometry by Stephen S. Kudla

The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry.


s 56Pages

Arithmetic Geometry Lecture Notes

This lecture note explains everything about Arithmetic Geometry.


s NAPages

Introduction to Arithmetic Geometry

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.


s 70Pages