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1 results

  • On the center of the ring of differential operators on a smooth variety over ℤ/pnℤ

  • Part of
  • Allen Stewart, Vadim Vologodsky
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 1 / January 2013
    Published online by Cambridge University Press:
    31 October 2012, pp. 63-80
    Print publication:
    January 2013
    • Article
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  • We compute the center of the ring of PD differential operators on a smooth variety over ℤ/pnℤ, confirming a conjecture of Kaledin (private communication). More generally, given an associative algebra A0 over ℤp and its flat deformation An over ℤ/pn+1ℤ, we prove that under a certain non-degeneracy condition, the center of An is isomorphic to the ring of length-(n+1) Witt vectors over the center of A0.