Abstract
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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Bell, J.P., Ingalls, C. & Ramkumar, R. Embeddings of quotient division algebras of rings of differential operators. Isr. J. Math. 219, 411–430 (2017). https://doi.org/10.1007/s11856-017-1485-z
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DOI: https://doi.org/10.1007/s11856-017-1485-z