By Alexander Polishchuk

The purpose of this e-book is to provide a contemporary remedy of the speculation of theta services within the context of algebraic geometry. the newness of its technique lies within the systematic use of the Fourier-Mukai rework. the writer starts off by way of discussing the classical idea of theta features from the viewpoint of the illustration idea of the Heisenberg staff (in which the standard Fourier remodel performs the widespread role). He then exhibits that during the algebraic method of this idea, the Fourier–Mukai remodel can usually be used to simplify the prevailing proofs or to supply thoroughly new proofs of many vital theorems. Graduate scholars and researchers with powerful curiosity in algebraic geometry will locate a lot of curiosity during this quantity.

**Read Online or Download Abelian varieties and the Fourier transform PDF**

**Similar algebraic geometry books**

**D. Gieseker's Lectures on moduli of curves PDF**

Those notes are according to a few lectures given at TIFR in the course of January and February 1980. the thing of the lectures used to be to build a projectire moduli area for strong curves of genus g >= 2 utilizing Mumford's geometric' invariant concept.

**New PDF release: p-Adic Automorphic Forms on Shimura Varieties**

This e-book covers the subsequent 3 themes in a way available to graduate scholars who've an figuring out of algebraic quantity idea and scheme theoretic algebraic geometry:1. An undemanding building of Shimura forms as moduli of abelian schemes. 2. p-adic deformation concept of automorphic types on Shimura kinds.

**Records: Mathematical Theory - download pdf or read online**

Drawing seriously from his personal classes on order statistics and files, Nevzorov (mathematics and mechanics, St. Petersburg U. ) deals introduces the idea of files to scholars with basically commonplace classes on chance concept and mathematical facts. He means that the tools for reading documents, the varied checklist types, and some of the functions he describes will be utilized by engineers and execs in different fields that use facts in addition to by way of mathematicians.

**Meinolf Geck's An Introduction to Algebraic Geometry and Algebraic Groups PDF**

An available textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first principles.

Building at the historical past fabric from algebraic geometry and algebraic teams, the textual content offers an creation to extra complicated and specialized fabric. An instance is the illustration idea of finite teams of Lie type.

The textual content covers the conjugacy of Borel subgroups and maximal tori, the idea of algebraic teams with a BN-pair, an intensive therapy of Frobenius maps on affine forms and algebraic teams, zeta features and Lefschetz numbers for kinds over finite fields. specialists within the box will get pleasure from a number of the new ways to classical results.

The textual content makes use of algebraic teams because the major examples, together with labored out examples, instructive routines, in addition to bibliographical and historic comments.

- Groupoid metrization theory : with applications to analysis on quasi-metric spaces and functional analysis
- Convex Polytopes
- C*-algebras and W*-algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete)
- Classification of Algebraic Varieties
- Ample Subvarieties of Algebraic Varieties
- Rational Algebraic Curves: A Computer Algebra Approach

**Additional resources for Abelian varieties and the Fourier transform**

**Example text**

20]); there, the generalization of manifolds studied is in terms of the commutative ring of smooth functions defined on a manifold. Here, we are looking instead at a generalization of the structure given by the smooth functions defined with domain an open subset of an arbitrary Hausdorff, complete, locally convex topological vector space and with range a fixed manifold. In section 2 we give details on our construction of a diffeological Lie group A(A), corresponding to a generalized symmetrized Cartan matrix A with a possibly countably infinite number of rows and columns such that the rows and columns are uniformly £2 bounded.

Sternberg, On the structure of a local homeomorphism, Amer. J. Math. 80 (1958) , 623-631. 31. S. Sternberg, Infinite Lie groups and the formal aspects of dynamical systems J. , vol. 10, No. 3 (1961), 451-474. 32. S. Swierczkowski, The path-functor on Banach Lie algebras, Proc. Konink. Nederl. Akad. , Ser A-74, N°3 (1971), 235-239. 33. T. van. Local and global groups I, Nederl Akad Wetensch Proc Ser A-65 Indagationes Math. 24, (1962), 391-425. 34. T. J. Korthagen, Nonenlargeable lie algebras, Proc.

Math. vol. 2, (1981), 365-397. 23. J. S. 3, (1974), 503-505. 24. L. Pontrjagin, Topological groups, Princeton University Press, fifth printing, 1958. 25. T. Robart, Groupes de Lie de dimension infinie. second et troisieme theoremes de Lie. ce, C. R. Acad. Sci. Paris, Serie I 322 (1996), 1071-1074. 26. T. Robart, Sur I'integrabilite des sous-algebres de Lie en dimension infinie, Can. J. , vol. 49 (4), 1997 pp. 820-839. 27. T. Robart, On Milnor's regularity and the path functor for the class of infinite dimensional Lie algebras of CBH type, Algebras, Groups and Geometries 16, 1998.

### Abelian varieties and the Fourier transform by Alexander Polishchuk

by Anthony

4.1