Logarithmic growth and Frobenius filtrations for solutions of p-adic differential equations

Bruno Chiarellotto, Nobuo Tsuzuki

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


For a ∇-module M over the ring K [[x]]0 of bounded functions over a p-adic local field K we define the notion of special and generic log-growth filtrations on the base of the power series development of the solutions and horizontal sections. Moreover, if M also admits a Frobenius structure then it is endowed with generic and special Frobenius slope filtrations. We will show that in the case of M a ψ-∇-module of rank 2, the Frobenius polygon for M and the log-growth polygon for its dual, Mv, coincide, this is proved by showing explicit relationships between the filtrations. This will lead us to formulate some conjectural links between the behaviours of the filtrations arising from the log-growth and Frobenius structures of the differential module. This coincidence between the two polygons was only known for the hypergeometric cases by Dwork.

Original languageEnglish
Pages (from-to)465-505
Number of pages41
JournalJournal of the Institute of Mathematics of Jussieu
Issue number3
Publication statusPublished - 2009


  • Logarithmic growth
  • Newton polygons
  • P-adic differential equations


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