# The Frobenius and monodromy operators for curves and abelian varieties

@article{Coleman1997TheFA,
title={The Frobenius and monodromy operators for curves and abelian varieties},
author={Robert F. Coleman and Adrian Iovita},
journal={Duke Mathematical Journal},
year={1997},
volume={97},
pages={171-215}
}
• Published 2 January 1997
• Mathematics
• Duke Mathematical Journal
In this paper, we give explicit descriptions of Hyodo and Kato's Frobenius and Monodromy operators on the first $p$-adic de Rham cohomology groups of curves and Abelian varieties with semi-stable reduction over local fields of mixed characteristic. This paper was motivated by the first author's paper "A $p$-adic Shimura isomorphism and periods of modular forms," where conjectural definitions of these operators for curves with semi-stable reduction were given.
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