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1 November 2019 Duality and nearby cycles over general bases
Qing Lu, Weizhe Zheng
Duke Math. J. 168(16): 3135-3213 (1 November 2019). DOI: 10.1215/00127094-2019-0057

Abstract

This paper studies the sliced nearby cycle functor and its commutation with duality. Over a Henselian discrete valuation ring, we show that this commutation holds, confirming a prediction of Deligne. As an application we give a new proof of Beilinson’s theorem that the vanishing cycle functor commutes with duality up to twist. Over an excellent base scheme, we show that the sliced nearby cycle functor commutes with duality up to modification of the base. We deduce that duality preserves universal local acyclicity over an excellent regular base. We also present Gabber’s theorem that local acyclicity implies universal local acyclicity over a Noetherian base.

Citation

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Qing Lu. Weizhe Zheng. "Duality and nearby cycles over general bases." Duke Math. J. 168 (16) 3135 - 3213, 1 November 2019. https://doi.org/10.1215/00127094-2019-0057

Information

Received: 10 April 2018; Revised: 1 April 2019; Published: 1 November 2019
First available in Project Euclid: 24 October 2019

zbMATH: 07154837
MathSciNet: MR4027830
Digital Object Identifier: 10.1215/00127094-2019-0057

Subjects:
Primary: 14F20
Secondary: 18F10, 32S30

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 16 • 1 November 2019
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