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The
stable cohomology of the Satake compactification of
$\mathcal{A}_g$
Jiaming Chen and Eduard Looijenga |
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Geometry & Topology 21 (2017) 2231–2241
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Abstract |
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Charney and Lee have shown that the rational cohomology of the Satake–Baily–Borel compactification of stabilizes as and they computed this stable cohomology as a Hopf algebra. We give a relatively simple algebrogeometric proof of their theorem and show that this stable cohomology comes with a mixed Hodge structure of which we determine the Hodge numbers. We find that the mixed Hodge structure on the primitive cohomology in degrees with is an extension of by ; in particular, it is not pure. |
Keywords
Satake compactification, stable cohomology, mixed Hodge
structure
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Mathematical Subject Classification 2010
Primary: 14G35, 32S35
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References |
Publication
Received: 3 November 2015
Accepted: 10 August 2016
Published: 19 May 2017
Proposed: Benson Farb
Seconded: Jim Bryan, Dan Abramovich
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Authors |
| Jiaming Chen | |
| Institut de mathématiques de
Jussieu-Paris Rive Gauche Université Paris 7 Diderot Campus de Grands Moulins Bureau 745 Bâtiment Sophie Germain 75205 Paris Cedex 13 France |
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| Eduard Looijenga | |
| Yau Mathematical Sciences
Center Tsinghua University Jin Chun Yuan West Building Haidian District Beijing, 100084 China |
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