The Frobenius and monodromy operators for curves and abelian varieties

1997/01/02 by Robert F. Coleman, Robert Coleman, Coleman, Robert +2 · 2 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/9701229

arxiv created 1997/01/02 · openalex publication_date 1997/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Kummer-faithfulness over p-adic fields
• Arithmetic monodromy of hyper-Kähler varieties over p-adic fields

Related

• Motivic monodromy and p-adic cohomology theories
• Monodromy representations of p-adic differential equations in families
• Semisimplicity and weight-monodromy for fundamental groups
• Stable models of Hecke operators
• Groupes de monodromie finie des variétés abéliennes