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15 March 2017 On the Tate and Mumford–Tate conjectures in codimension 1 for varieties with h2,0=1
Ben Moonen
Duke Math. J. 166(4): 739-799 (15 March 2017). DOI: 10.1215/00127094-3774386

Abstract

We prove the Tate conjecture for divisor classes and the Mumford–Tate conjecture for the cohomology in degree 2 for varieties with h2,0=1 over a finitely generated field of characteristic 0, under a mild assumption on their moduli. As an application of this general result, we prove the Tate and Mumford–Tate conjectures for several classes of algebraic surfaces with pg=1.

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Ben Moonen. "On the Tate and Mumford–Tate conjectures in codimension 1 for varieties with h2,0=1." Duke Math. J. 166 (4) 739 - 799, 15 March 2017. https://doi.org/10.1215/00127094-3774386

Information

Received: 21 September 2015; Revised: 21 April 2016; Published: 15 March 2017
First available in Project Euclid: 9 December 2016

zbMATH: 1372.14008
MathSciNet: MR3619305
Digital Object Identifier: 10.1215/00127094-3774386

Subjects:
Primary: 14C
Secondary: 14D, 14J20

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 4 • 15 March 2017
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