On bt1 group schemes and fermat curves

Rachel Pries, Douglas Ulmer

Research output: Contribution to journalArticlepeer-review

Abstract

Let p be a prime number and let k be an algebraically closed field of characteristic p. A BT1 group scheme over k is a finite commutative group scheme which arises as the kernel of p on a p-divisible (Barsotti–Tate) group. We compare three classifications of BT1 group schemes, due in large part to Kraft, Ekedahl, and Oort, and defined using words, canonical filtrations, and permutations. Using this comparison, we determine the Ekedahl–Oort types of Fermat quotient curves and we compute four invariants of the p-torsion group schemes of these curves.

Original languageEnglish (US)
Pages (from-to)705-739
Number of pages35
JournalNew York Journal of Mathematics
Volume27
StatePublished - 2021

Keywords

  • Abelian variety
  • Curve
  • De rham cohomology
  • Dieudonné module
  • Ekedahl–oort type
  • Fermat curve
  • Finite field
  • Frobenius
  • Group scheme
  • Jacobian
  • Verschiebung

ASJC Scopus subject areas

  • Mathematics(all)

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