Download Abelian Varieties, Theta Functions and the Fourier Transform by Alexander Polishchuk PDF

By Alexander Polishchuk

the purpose of this ebook is to offer a latest remedy of the idea of theta features within the context of algebraic geometry. the newness of its procedure lies within the systematic use of the Fourier-Mukai rework. the writer begins through discussing the classical idea of theta services from the viewpoint of the illustration conception of the Heisenberg crew (in which the standard Fourier rework performs the in demand role). He then indicates that during the algebraic method of this conception, the Fourier–Mukai rework can usually be used to simplify the present proofs or to supply thoroughly new proofs of many very important theorems. Graduate scholars and researchers with robust curiosity in algebraic geometry will locate a lot of curiosity during this volume.

Show description

Read or Download Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics) PDF

Best number theory books

Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications (Chapman & Hall Pure and Applied Mathematics)

First constructed within the early Eighties via Lenstra, Lenstra, and Lovász, the LLL set of rules used to be initially used to supply a polynomial-time set of rules for factoring polynomials with rational coefficients. It in a short time turned a vital software in integer linear programming difficulties and was once later tailored to be used in cryptanalysis.

The Arithmetic of Elliptic Curves: 106 (Graduate Texts in Mathematics)

The idea of elliptic curves is unusual through its lengthy historical past and by way of the range of the equipment which were utilized in its examine. This publication treats the mathematics procedure in its sleek formula, by using uncomplicated algebraic quantity concept and algebraic geometry. Following a short dialogue of the required algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal crew of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields.

Algebraic Operads: An Algorithmic Companion

Algebraic Operads: An Algorithmic significant other provides a scientific remedy of Gröbner bases in numerous contexts. The e-book builds as much as the speculation of Gröbner bases for operads as a result of the moment writer and Khoroshkin in addition to a variety of functions of the corresponding diamond lemmas in algebra. The authors current quite a few subject matters together with: noncommutative Gröbner bases and their functions to the development of common enveloping algebras; Gröbner bases for shuffle algebras that are used to resolve questions on combinatorics of diversifications; and operadic Gröbner bases, very important for purposes to algebraic topology, and homological and homotopical algebra.

Geometry, Analysis and Probability: In Honor of Jean-Michel Bismut (Progress in Mathematics)

This quantity provides unique study articles and prolonged surveys with regards to the mathematical curiosity and paintings of Jean-Michel Bismut. His striking contributions to chance idea and international research on manifolds have had a profound effect on numerous branches of arithmetic within the components of regulate idea, mathematical physics and mathematics geometry.

Extra info for Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics)

Sample text

Download PDF sample

Rated 4.55 of 5 – based on 11 votes
 

Author: admin