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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It exists, it is the Fourier-Deligne transform. Where to Go from Here References Index. Generally, for XY X,Y two suitably well-behaved schemes e.
The Fourier-Mukai transform is a categorified integral transform roughly similar to the standard Fourier transform. This site is running on Instiki 0.
big picture – Heuristic behind the Fourier-Mukai transform – MathOverflow
Huybrechts Abstract This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Users without a subscription are not able to see the full content. However I don’t know enough to say anything more than that. Thanks, that looks very interesting. That equivalence is analogous to the fouriier Fourier transform that gives an isomorphism between transformms distributions on a finite-dimensional real vector space and its dual.
Such concept of integral transform is rather general and may be considered also in derived algebraic geometry e. To purchase, visit your preferred ebook provider.
Don’t have an account? What is the connection to the classical Fourier transform? Daniel HuybrechtsFourier-Mukai transformspdf.
This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. I really know almost nothing about the classical Fourier transform, but mukak of the main points is that the Fourier transform is supposed to be an invertible operation.
For a morphism f: I believe you do the Fourier transform 4 times to get your original function back. Hence this is a pull-tensor-push integral transform through the product correspondence.
Fourier-Mukai Transforms in Algebraic Geometry – Daniel Huybrechts – Oxford University Press
There are some cool theorems of Orlov, I forget the precise statements but you can probably easily find them in any of the books suggested so farwhich say that in certain cases any derived equivalence is induced by a Fourier-Mukai transform. Csar Lozano Huerta 1, 1 15 geo,etry Civil War American History: Classical, Early, and Medieval Prose and Writers: Moreover, could someone recommend a concise introduction to the subject?
Just as CommRing behaves a lot like Set opI think there is probably some kind of general phenomenon that sheaves or vector bundles behave a lot like functions, which is what’s happening here. Classical, Early, and Medieval World History: Last revised on August 4, at A Clarendon Press Publication. The final chapter summarizes recent research mykai, such as connections to orbifolds and the representation theory of finite groups via the Trabsforms correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.
Oxford Scholarship Online This book is available as part of Oxford Scholarship Online – view abstracts and keywords at book and chapter level. Remark It was believed that theorem should be true kn all triangulated functors e.
The fact that the function associated to 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.
Fourier-Mukai Transforms in Algebraic Geometry
This dictionnary was one of the motivation for the formulation of the geometric Langlands program see some expository articles of Frenkel for example. And of course because it was studied by Mukai. In string theory, T-duality short for target space dualitywhich relates two quantum field theories or string theories with different spacetime geometries, is closely related with the Fourier-Mukai transformation, a fact that has been greatly explored recently. I second Kevin’s suggestion of Huybrechts’ book, but if you want to to look at something shorter first I recommend the notes by Hille and van den Bergh.
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