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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 1, Pages 165–200 (Mi izv189)  

This article is cited in 2 scientific papers (total in 2 papers)

On Frobenius traces

S. G. Tankeev

Vladimir State University

Abstract: In this paper we discuss a certain Diophantine property of Frobenius traces associated with an Abelian variety over a number field $k$ and apply it to prove the Mumford–Tate conjecture for 4$p$-dimensional Abelian varieties $J$ over $k$, where $p$ is a prime number, $p\geqslant 17$, or (under certain weak assumptions) $\operatorname{End}^0(J\otimes\overline k)$ is an imaginary quadratic extension of $\mathbb Q$.

DOI: https://doi.org/10.4213/im189

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English version:
Izvestiya: Mathematics, 1998, 62:1, 157–190

Bibliographic databases:

MSC: 14K15, 14G20
Received: 05.03.1996

Citation: S. G. Tankeev, “On Frobenius traces”, Izv. RAN. Ser. Mat., 62:1 (1998), 165–200; Izv. Math., 62:1 (1998), 157–190

Citation in format AMSBIB
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\pages 165--200
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  • http://mi.mathnet.ru/eng/izv189
  • https://doi.org/10.4213/im189
  • http://mi.mathnet.ru/eng/izv/v62/i1/p165

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. G. Tankeev, “Cycles of small codimension on a simple $2p$- or $4p$-dimensional Abelian variety”, Izv. Math., 63:6 (1999), 1221–1262  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. G. Tankeev, “On weights of the $l$-adic representation and arithmetic of Frobenius eigenvalues”, Izv. Math., 63:1 (1999), 181–218  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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