Israel Journal of Mathematics

, Volume 219, Issue 1, pp 411–430 | Cite as

Embeddings of quotient division algebras of rings of differential operators

  • Jason P. Bell
  • Colin Ingalls
  • Ritvik Ramkumar


Let k be an algebraically closed field of characteristic zero, let X and Y be smooth irreducible algebraic curves over k, and let D(X) and D(Y) denote respectively the quotient division rings of the ring of differential operators of X and Y. We show that if there is a k-algebra embedding of D(X) into D(Y), then the genus of X must be less than or equal to the genus of Y, answering a question of the first-named author and Smoktunowicz.


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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  • Jason P. Bell
    • 1
  • Colin Ingalls
    • 2
  • Ritvik Ramkumar
    • 3
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterloo, ONCanada
  2. 2.Department of Mathematics and StatisticsUniversity of New BrunswickFredricton, NBCanada
  3. 3.Department of MathematicsUniversity of California, BerkeleyBerkeley, CAUSA

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