The Frobenius and Monodromy operators for Curves and Abelian Varieties, by Robert Coleman and Adrian Iovita

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.

Robert Coleman and Adrian Iovita <coleman@math.berkeley.edu, iovita@scylla.math.mcgill.ca>