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 book is available as part of Oxford Scholarship Online – view abstracts and algebraicc at book and chapter level. Discussion in the context of geometric Langlands duality is in.
Huybrechts, author Mathematisches Institut, Universitaet Bonn. Tensor product of sheaves behave a lot like multiplication of functions Classical, Early, and Medieval World History: Hodge theoryHodge theorem. Such concept of integral transform is rather general and may be considered also in derived algebraic geometry e. Classical, Early, and Medieval Plays and Playwrights: You may also be interested in reading about Pontryagin dualitywhich is a version of the Fourier transform for locally compact abelian topological groups this is obviously quite similar, at least superficially, to Mukai’s result about abelian varieties.
Let g denote the dimension of X. Hopefully somebody else can say something about that. Journal of High Energy Physics.
Including notions from other areas, e. From Wikipedia, the free encyclopedia.
Fourier-Mukai Transforms in Algebraic Geometry
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. This dictionnary was one of the motivation for the formulation of the geometric Langlands program see some expository articles of Frenkel for example.
It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. 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.
Heuristic behind the Fourier-Mukai transform Ask Question.
Fourier–Mukai transform
Banerjee and Hudson have defined Fourier-Mukai functors analogously on algebraic cobordism. Derived category and Canonical Bundle I 5. Remark It was believed that theorem should be true for all triangulated functors e. Sign up or log in Sign up using Google. MathOverflow works best with JavaScript enabled.
And so we have to work with the derived categories. It interchanges Pontrjagin product and tensor product. See the history of this page for a list of all contributions to it.
Views Read Edit View history. This site is running on Instiki 0. Email Required, but never shown. 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 for details see www. Including notions from other areas, e.
Fourier-Mukai transform in nLab
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. I believe you algebeaic the Fourier transform 4 times to get your original function back. There is a case where the analogy between sheaves and functions is more than analogy: Retrieved from ” https: Sign up using Facebook.
By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. I think Huybrechts’ book “Fourier-Mukai transforms in algebraic geometry” is a good book to look at.
Derived Category and Canonical bundle II 7.
Fourier-Mukai transforms in algebraic geometry / D. Huybrechts – Details – Trove
This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.
Most natural functors, including basic ones like pushforwards and pullbacksare of this type. Home Questions Tags Users Unanswered. Dmitri OrlovDerived categories of coherent sheaves and equivalences between themRussian Math.
Let me give a rough picture of the Fourier-Mukai transform and how it resembles the classical situation.
