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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Front Matter Title Pages Preface. I think Huybrechts’ book “Fourier-Mukai transforms in algebraic geometry” is a good book to look at. Hence this is a pull-tensor-push integral transform through the product correspondence. Generally, for XY X,Y two suitably well-behaved schemes e. This also happens to fouridr one of my favourite books.
I think this was proven by Mukai. However I don’t know enough to say anything more than that. Equivalence Criteria for Fourier-Mukai Transforms 8. Advances in Theoretical and Mathematical Physics. Publications Pages Publications Pages. Introduction to Abstract Homotopy Theory. Ilya Nikokoshev 8, 9 60 Where to Go from Kn References Index. Including notions from other areas, e.
Banerjee and Hudson have defined Fourier-Mukai functors analogously on algebraic cobordism. Overview Description Table of Contents. Generators and representability of functors in commutative and noncommutative geometry, arXiv.
As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of The following answers might be useful: Don’t have an account? For a morphism f: Moreover, could someone recommend a concise introduction to the subject? What is the umkai idea behind the Fourier-Mukai transform? From Wikipedia, the free encyclopedia. That equivalence is analogous to the zlgebraic Fourier transform that gives an isomorphism between tempered distributions on a finite-dimensional real vector space and its dual.
Note that the converse is not true: Alexei BondalMichel van den Bergh. Thanks, that looks very interesting.
Pi-algebraspherical object and Pi A -algebra. Post as a guest Name. I think this is supposed to be analogous to the statement I made about the classical Fourier transform being invertible.
BenZvi-Nadler-Preygel 13 and lots of other contexts. The pushforward of a coherent sheaf is not always coherent. Foliations and the Geometry of 3-Manifolds Danny Calegari. Derived Category and Canonical bundle II 7.
Fourier-Mukai Transforms in Algebraic Geometry – Daniel Huybrechts – Oxford University Press
This dictionnary was one of the motivation for the formulation of the geometric Foureir program see some expository articles of Frenkel for example. Nagoya Mathematical Journal Just a complement to the answer of Kevin Lin. It was believed that theorem should be true for all triangulated functors e.
Pullback fojrier sheaves behave a lot like pullback of functions This site is running on Instiki 0. It’s something like this: This book is available as part of Oxford Scholarship Online – view abstracts and keywords at book and chapter level. 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.
Oxford Scholarship Online This book is available as part of Oxford Scholarship Online – view abstracts and keywords at book and chapter level. Fourier-Mukai transform – a first example Intuition for Integral Transforms Fourier transform for dummies The last one has my sketch of an answer which I’ll post here once it gets better. 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.
Introduction to Basic Homotopy Theory. Subscriber Login Email Address. This page was last edited on 20 Septemberat Hochschild cohomologycyclic cohomology. Lin Dec 30 ’09 at Academic Skip to main content. And of course because it was studied by Mukai.