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Deformations of nilpotent matrices over rings and reduction of analytic families of meromorphic differential equations

About this Title

Donald G. Babbitt and V. S. Varadarajan

Publication: Memoirs of the American Mathematical Society
Publication Year: 1985; Volume 55, Number 325
ISBNs: 978-0-8218-2326-2 (print); 978-1-4704-0738-4 (online)
DOI: https://doi.org/10.1090/memo/0325
MathSciNet review: 787539
MSC: Primary 12H05; Secondary 14D05, 22E65, 34A20

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Table of Contents

Chapters

  • 1. Introduction
  • Nilpotent matrices over integral domains: Structure and deformation
  • 2. The invariants $\ell _j$
  • 3. Local deformations of endomorphisms and modules over discrete valuation rings
  • 4. Upper semicontinuity of $\underset {\tilde {}}{\ell }$. Structure of deformations with constant $\underset {\tilde {}}{\ell }$
  • 5. Admissible nilpotents and their transversal deformations
  • Reduction theory of connections over integrally closed Noetherian domains
  • 6. Generalities and preliminaries
  • 7. Connections over Dedekind domains
  • 8. The general case: reduction in the category of differential modules
  • Reduction of connections over $\mathcal {O}_d$
  • 9. The main theorem for well-behaved connections over $\mathcal {O}_d$
  • 10. Reduction of regulated connections
  • Appendix