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Analytic theory of Abelian varieties

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Published by University Press in Cambridge .
Written in English

Subjects:

  • Abelian varieties,
  • Riemann surfaces,
  • Functions, Meromorphic

Book details:

Edition Notes

StatementH. P. F. Swinnerton-Dyer.
SeriesLondon Mathematical Society lecture note series ;, 14
Classifications
LC ClassificationsQA564 .S94
The Physical Object
Paginationvii, 90 p. ;
Number of Pages90
ID Numbers
Open LibraryOL5069343M
ISBN 100521205263
LC Control Number74077835

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Get this from a library! Analytic theory of Abelian varieties. [H P F Swinnerton-Dyer] -- The study of abelian manifolds forms a natural generalization of the theory of elliptic functions, that is, of doubly periodic functions of one complex variable. When an abelian manifold is embedded. Analytic theory of Abelian varieties H. P. F. Swinnerton-Dyer The study of abelian manifolds forms a natural generalization of the theory of elliptic functions, that is, of doubly periodic functions of one complex variable. By H. P. F. Swinnerton‐Dyer: pp. £ (Cambridge University Press, ). Mumford, D. Abelian Varieties, Oxford University Press: Oxford, (2nd edn ). Chapter I treats the analytic theory using line bundles instead of divisors. Most of the book gives a general treatment of abelian varieties from the point of view of schemes. zbMATH Google Scholar.

Lecture 2: Abelian varieties The subject of abelian varieties is vast. In these notes we will hit some highlights of the theory, stressing examples and intuition rather than proofs (due to lack of time, among other reasons). We will note analogies with the more concrete case of elliptic curves (as in [Si]), as. analytic theory of Lie groups, so one has to look at higher-order data. But even in these algebraic cases, the theory is guided by the analytic analogy. Link between complex abelian varieties and complex tori. Here is an important fact (proved by Serre under projectivity hypotheses, from . The program will follow closely the book Analytic theory of abelian varieties, H.P.F. Swinnerton-Dyer, with some additional material taken from chapter 1 of Abelian varieties, D. Mumford, and some applications taken from Curves and their Jacobians, D. Mumford if time permits, We will discuss the program of lectures (by the participants) in. This book provides a modern, i.e., scheme-theoretic, treatment of most of the basic theory of abelian varieties. Chapter 1 is devoted to the analytic theory of abelian varieties over the complex numbers.

The contents of the book are as follows: Part I gives the basic "classical theory", including Hecke operators and the Petersson scalar product. An appendix proves the Eichler-Selberg trace formula for the Hecke operators on SL_2(Z), which expresses this trace . This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. " far more readable than most it is also much more complete.". A very classical introduction is Swinnerton-Dyer's Analytic theory of abelian varieties (London Mathematical Society Lecture Note Series 14). Another good place to start is M. Schlichenmaier, An introduction to Riemann surfaces, algebraic curves and moduli spaces, Theoretical and Mathematical Physics, Springer-Verlag (2nd ed.). Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link).