Geodesic
On Frobenius traces
Izvestiya. Mathematics , Tome 62 (1998) no. 1, pp. 157-190

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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 $\mathbb Q$. 
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     author = {S. G. Tankeev},
     title = {On {Frobenius} traces},
     journal = {Izvestiya. Mathematics },
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     number = {1},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_1_a4/}
}
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S. G. Tankeev. On Frobenius traces. Izvestiya. Mathematics , Tome 62 (1998) no. 1, pp. 157-190. http://geodesic.mathdoc.fr/item/IM2_1998_62_1_a4/