On rings of commuting partial differential operators

Zheglov, A.

doi:10.1090/S1061-0022-2014-01316-7

On rings of commuting partial differential operators
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by A. B. Zheglov
Translated by: the author

St. Petersburg Math. J. 25 (2014), 775-814

DOI: https://doi.org/10.1090/S1061-0022-2014-01316-7

Published electronically: July 18, 2014

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Abstract:

A natural generalization is given for the classification of commutative rings of ordinary differential operators, as presented by Krichever, Mumford, Mulase. The commutative rings of operators in a completed ring of partial differential operators in two variables (satisfying certain mild conditions) are classified in terms of Parshin’s generalized geometric data. This classification involves a generalization of M. Sato’s theory and is constructible both ways.

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