Canonical lifts and δ-structures

• James Borger ^[1] ; Lance Gurney ^[1]
  1. [1] Australian National University

     Australian National University

     Australia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 5, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00599-x
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• Resumen

  • We extend the Serre–Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a p-adic formal scheme S. We show that the canonical lift is the unique lift to W(S) which admits a δ-structure in the sense of Joyal, Buium, and Bousfield. We prove analogous statements for families of ordinary p-groups and p-divisible groups.