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}
}
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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References

SHOWING 1-10 OF 37 REFERENCES
p-Adic abelian integrals and commutative lie groups
The aim of this paper is to propose an ``elementary" approach to Coleman's theory of p-adic abelian integrals. Our main tool is a theory of commutative p-adic Lie groups (the logarithm map); we use
Torsion points on curves and p-adic Abelian integrals
THEOREM A. Let f: C --* J be an Albanese morphism defined over a number field K, of a s-mooth curve of genus g into its Jacobian. Suppose J has potential complex multiplication. Let S denote the set
Some consequences of the Riemann hypothesis for varieties over finite fields
We deduce from Deligne's form of the Riemann hypothesis and the hard Lefschetz theoreminl-adic cohomology the corresponding facts for any “reasonable” cohomology theory, in particular for crystalline
Formal Cohomology: II. The Cohomology Sequence of a Pair
Now Grothendieck has shown that the cohomology of a complex variety may be defined algebraically; in particular if X is a complex affine variety the canonical map from the closed/exact algebraic
Sur certains types de representations p-adiques du groupe de Galois d'un corps local; construction d'un anneau de Barsotti-Tate
1. Representations de Hodge-Tate 532 2. Construction du corps BDR 534 3. Representations de de Rham 545 4. L'anneau B 549 5. Representations cristallines et potentiellement cristallines .. 560 6.
Periods and duality of $p$-adic Barsotti-Tate groups
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
Reciprocity laws on curves
© Foundation Compositio Mathematica, 1989, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions
...
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