Embeddings of quotient division algebras of rings of differential operators
| Autor: | Ritvik Ramkumar, Jason P. Bell, Colin Ingalls |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Ring (mathematics)
General Mathematics 010102 general mathematics Zero (complex analysis) 14A22 16S38 16W50 16P90 0102 computer and information sciences Mathematics - Rings and Algebras Differential operator 01 natural sciences Combinatorics 010201 computation theory & mathematics Rings and Algebras (math.RA) Genus (mathematics) FOS: Mathematics Embedding Algebraic curve 0101 mathematics Algebraically closed field Quotient Mathematics |
| DOI: | 10.48550/arxiv.1411.3574 |
| Popis: | 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. Comment: 11 pages |
| Databáze: | OpenAIRE |
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