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math.AGNov 14, 1999
39
citations (OpenAlex)
authors
  • A. N. Parshin
arXiv abstractPDF
paper

On a Ring of Formal Pseudo-differential Operators

arXiv:math/9911098

Abstract

We study the notion of non-commumative higher dimensional local fields. A simplest example is the ring P of formal pseudo- differential operators. As an application we extend the KP hierarchy to the space Pn.

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Cited by in corpus (15)

  • Krichever correspondence for algebraic varieties
  • Representations of Higher Adelic Groups and Arithmetic
  • Commuting differential operators and higher-dimensional algebraic varieties
  • On some questions related to the Krichever correspondence
  • Krichever Correspondence for Algebraic Surfaces
  • Differential Equations of Genus Four Hyperelliptic ℘ Functions
  • Geometric properties of commutative subalgebras of partial differential operators
  • Geometric algebra and quadrilateral lattices
  • On rings of commuting partial differential operators
  • Formal punctured ribbons and two-dimensional local fields
  • Generalized KP Hierarchy for Several Variables
  • Tau functions associated to pseudodifferential operators of several variables
  • Invitation to higher local fields, Part II, section 8: Higher local skew fields
  • Integrable systems and local fields
  • Geometry of cross ratio
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