A geometric Jacquet–Langlands correspondence for paramodular Siegel threefolds
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AbstractWe study the Picard–Lefschetz formula for Siegel modular threefolds of paramodular level and prove the weight-monodromy conjecture for its middle degree inner cohomology. We give some applications to the Langlands programme: using Rapoport-Zink uniformisation of the supersingular locus of the special fiber, we construct a geometric Jacquet–Langlands correspondence between $${\text {GSp}}_4$$ GSp 4 and a definite inner form, proving a conjecture of Ibukiyama. We also prove an integral version of the weight-monodromy conjecture and use it to deduce a level lowering result for cohomological cuspidal automorphic representations of $${\text {GSp}}_4$$ GSp 4 .
2009 ◽
Vol 2009
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pp. 1-14
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2014 ◽
Vol 150
(4)
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pp. 523-567
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2009 ◽
Vol 8
(4)
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pp. 693-741
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2016 ◽
Vol 152
(7)
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pp. 1476-1488
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2014 ◽
Vol 10
(04)
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pp. 963-1013
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2013 ◽
Vol 150
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pp. 191-228
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2010 ◽
Vol 146
(5)
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pp. 1115-1164
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