Download e-book for iPad: Abelian varieties and the Fourier transform by Alexander Polishchuk

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.

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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.

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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.

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