Mathematical Research Letters

Volume 14 (2007)

Number 1

Sato-Tate distribution for abelian varieties with real multiplication over function fields

Pages: 113 – 128

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n1.a10

Author

Chung Pang Mok (Harvard University)

Abstract

We calculate the monodromy groups of some universal families of abelian varieties with real multiplication by $\mathbf{Q}(\cos\frac{2\pi}{r})$, over certain Hilbert type modular varieties over finite fields. Using Deligne’s equidistribution theorem, we obtain the Sato-Tate law for the distribution of Frobenius eigenvalues of these universal families of abelian varieties.

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