This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the. Fourier-Mukai transforms in algebraic geometry. CHTS. Mathematisches Institut Universitat Bonn. CLARENDON PRESS • OXFORD. In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is.
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Lin Dec 30 ’09 at This site is running on Instiki 0. Let me give a rough picture of the Fourier-Mukai transform and how it resembles the classical situation. A Quick Tour 3. Classical, Early, and Medieval Plays and Playwrights: Hodge theoryHodge theorem. Tensor product of sheaves behave a lot like multiplication of functions For a morphism f: But there is certainly something deep going on.
To purchase, visit your preferred ebook provider. Generators and representability of functors in commutative and noncommutative geometry, arXiv. If X X is a moduli space of line bundles over a suitable algebraic curvethen a slight variant of the Fourier-Mukai transform is the geometric Langlands correspondence in the abelian case Frenkel 05, section 4.
Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Pieter Belmanssection 2. Under the terms of the umkai agreement, transfor,s individual user may print out a PDF of a single chapter of a monograph in OSO for personal use transsforms details see www.
Classical, Early, and Medieval World History: The Fourier-Mukai transform in algebraic geometry gets its name because it at least superficially resembles the classical Fourier transform.
It interchanges Pontrjagin product and tensor product. This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the Institut de Mathematiques de Jussieu in and And of course because it was studied by Mukai.
See the history of this page for a list of all contributions to it. The fact that the function associated transdorms the Fourier-Deligne transform of a sheaf is the usual Fourier transform of the function associated to the sheaf is a consequence of the Grothendieck trace formula. This dictionnary was one of the motivation for the formulation of the geometric Langlands program see some expository articles of Frenkel for example.
However according to RVdB this is not true. Journal of High Energy Physics. It’s something like this: That equivalence is analogous to the classical Fourier transform that gives an isomorphism between tempered distributions on a finite-dimensional real vector space and its dual. Sign up using Facebook.
Bibliographic Information Print publication date: Oxford Scholarship Online This book is available as part of Oxford Scholarship Online – view abstracts and keywords at book and chapter level. The pushforward of a coherent sheaf is not always coherent.
Classical, Early, and Medieval Poetry and Poets: A Clarendon Press Publication.
Hochschild cohomologycyclic cohomology. From Wikipedia, the free encyclopedia.
Fourier-Mukai Transforms in Algebraic Geometry – Oxford Scholarship
However I don’t know enough to say anything more than that. Advances in Theoretical and Mathematical Physics.
Oxford University Press is a department of the University of Oxford. Including tansforms from other areas, e.
Fourier-Mukai Transforms in Algebraic Geometry
Introduction to Abstract Homotopy Theory. This also happens to be one of my favourite books. Derived Category and Canonical bundle II 7.
This book is available tdansforms part of Oxford Scholarship Online – view abstracts and keywords at book and chapter level. Views Read Edit View history. But to make all of this foyrier work out, we have to actually use the derived pushforward, not just the pushforward. Users without a subscription are not able to see the full content. Ebook This title is available as an ebook. I believe you do the Fourier transform 4 times to get your original function back.
The Fourier-Mukai transform is a categorified integral transform roughly similar to the standard Fourier transform. I think this was proven by Mukai.
What is the connection to the classical Fourier transform?