15 October 2016 Partial Fourier–Mukai transform for integrable systems with applications to Hitchin fibration
Dima Arinkin, Roman Fedorov
Duke Math. J. 165(15): 2991-3042 (15 October 2016). DOI: 10.1215/00127094-3645223


Let X be an abelian scheme over a scheme B. The Fourier–Mukai transform gives an equivalence between the derived category of X and the derived category of the dual abelian scheme. We partially extend this to certain schemes X over B (which we call degenerate abelian schemes) whose generic fiber is an abelian variety, while special fibers are singular.

Our main result provides a fully faithful functor from a twist of the derived category of Picτ(X/B) to the derived category of X. Here Picτ(X/B) is the algebraic space classifying fiberwise numerically trivial line bundles.

Next, we show that every algebraically integrable system gives rise to a degenerate abelian scheme and discuss applications to Hitchin systems.


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Dima Arinkin. Roman Fedorov. "Partial Fourier–Mukai transform for integrable systems with applications to Hitchin fibration." Duke Math. J. 165 (15) 2991 - 3042, 15 October 2016. https://doi.org/10.1215/00127094-3645223


Received: 10 November 2014; Revised: 19 October 2015; Published: 15 October 2016
First available in Project Euclid: 16 August 2016

zbMATH: 06656239
MathSciNet: MR3557277
Digital Object Identifier: 10.1215/00127094-3645223

Primary: 14D24
Secondary: 14F05 , 14K30 , 14L15

Keywords: abelian scheme , Fourier–Mukai transform , Hitchin system , integrable system , Langlands duality , Picard space

Rights: Copyright © 2016 Duke University Press


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Vol.165 • No. 15 • 15 October 2016
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