Duke Mathematical Journal

On the Tate and Mumford–Tate conjectures in codimension 1 for varieties with h2,0=1

Ben Moonen

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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.

Article information

Source
Duke Math. J., Volume 166, Number 4 (2017), 739-799.

Dates
Received: 21 September 2015
Revised: 21 April 2016
First available in Project Euclid: 9 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1481252670

Digital Object Identifier
doi:10.1215/00127094-3774386

Mathematical Reviews number (MathSciNet)
MR3619305

Zentralblatt MATH identifier
1372.14008

Subjects
Primary: 14C
Secondary: 14D 14J20: Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]

Keywords
Tate conjecture Mumford–Tate conjecture motives

Citation

Moonen, Ben. On the Tate and Mumford–Tate conjectures in codimension $1$ for varieties with $h^{2,0}=1$. Duke Math. J. 166 (2017), no. 4, 739--799. doi:10.1215/00127094-3774386. https://projecteuclid.org/euclid.dmj/1481252670


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