Abstract
We study abelian varieties over finitely generated fields K of characteristic zero, whose \(\ell \)-adic Tate modules are isomorphic as Galois modules for all primes \(\ell \).
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Acknowledgements
Part of this work was done in May–June 2015 when the author was visiting Department of Mathematics of the Weizmann Institute of Science (Rehovot, Israel) and in May–June 2016 when the author was a visitor at the Max-Planck-Institut für Mathematik (Bonn, Germany). The hospitality and support of both Institutes are gratefully acknowledged.
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In memoriam of Bill Waterhouse (1941–2016)
The author is grateful to Jiangwei Xue for useful discussions, to Stefan Patrikis and Felipe Voloch for their interest in this paper and to the Simons Foundation for financial and moral support (via Grant # 246625 to Yuri Zarkhin).
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Zarhin, Y.G. Almost isomorphic abelian varieties. European Journal of Mathematics 3, 22–33 (2017). https://doi.org/10.1007/s40879-016-0122-4
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DOI: https://doi.org/10.1007/s40879-016-0122-4