The level of pairs of polynomials

Alberto F. Boix, Marc Paul Noordman, Jaap Top

Research output: Contribution to journalArticlepeer-review


Given a polynomial f with coefficients in a field of prime characteristic p, it is known that there exists a differential operator that raises (Formula presented.) to its pth power. We first discuss a relation between the “level” of this differential operator and the notion of “stratification” in the case of hyperelliptic curves. Next, we extend the notion of level to that of a pair of polynomials. We prove some basic properties and we compute this level in certain special cases. In particular, we present examples of polynomials g and f such that there is no differential operator raising g/f to its pth power.

Original languageEnglish
Pages (from-to)4235-4248
Number of pages14
JournalCommunications in Algebra
Issue number10
StatePublished - 2 Oct 2020


  • Differential operators
  • Frobenius map
  • first order differential equation
  • ordinary curve
  • prime characteristic
  • supersingular curve

ASJC Scopus subject areas

  • Algebra and Number Theory


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