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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This dictionnary was one of the motivation for the formulation of the geometric Langlands program see some expository articles of Frenkel for example. Huybrechts 08, page 4. What is the connection to the classical Fourier transform?

It’s something like this: Lin Dec 27 ’09 at 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.

However according to RVdB this is not true.

Fourier-Mukai Transforms in Algebraic Geometry

Print Save Cite Email Share. 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. Classical, Early, and Medieval Prose and Writers: By using this site, you agree to the Terms of Use and Privacy Policy. By using our site, you acknowledge that you transfprms read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.


Fourier-Mukai transform in nLab

But there is certainly something deep going on. Geometgy page was last edited on 20 Septemberat Hodge theoryHodge theorem. The Fourier—Mukai transformation is nearly involutive:.

Ilya Nikokoshev 8, 9 60 Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use algebrqic details see www. I really know almost nothing about the classical Fourier transform, but one of the main points is that the Fourier transform is supposed to be transformw invertible operation. Huybrechts Abstract This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view.

Fourier–Mukai transform

Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. GMRA 1, 2 23 Overview Description Table of Contents. This defines a algeebraic sheaf-function gekmetry with all the analogies cited by Kevin. Users without a subscription are not able to see the full content. Fourier-Mukai transform – a first example Intuition for Integral Transforms Mjkai transform for dummies The last one has my sketch of an answer which I’ll post here once it gets better.

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Dmitri OrlovDerived categories of coherent sheaves and equivalences between themRussian Math. Choose your country or region Close. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide.

Huybrechts, author Mathematisches Institut, Universitaet Bonn. Just a complement to the answer of Kevin Lin.

Fourier-Mukai Transforms in Algebraic Geometry – Daniel Huybrechts – Oxford University Press

Sign up using Facebook. Banerjee and Hudson have defined Fourier-Mukai functors analogously on algebraic cobordism.

Surveys, 583,translation. I think this was proven by Mukai. Though theorem is stated there for F F admitting a right adjointit follows from Bondal-van den Bergh that every triangulated fully faithful functor admits a right adjoint automatically see e.

You may want to look at Tom Bridgeland’s PhD thesis. A Clarendon Press Publication. Most natural functors, including basic ones like pushforwards and pullbacksare of this type. Daniel HuybrechtsFourier-Mukai transformspdf.