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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Symmetric nilpotent matrices with maximal rank and a conjecture of Grothendieck-Koblitz
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by Ching-Li Chai PDF
Proc. Amer. Math. Soc. 119 (1993), 87-95 Request permission

Abstract:

All pairs $(p,n)$ such that there exists an $n \times n$ symmetric matrix $A$ with entries in the ring ${\mathbb {Z}_p}$ of $p$-adic integers such that ${A^n} = p \cdot U$ with $U$ invertible in ${M_{n \times n}}({\mathbb {Z}_p})$ are determined. It is shown that such matrices $A$ can be used to construct examples of deformations of abelian varieties.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 119 (1993), 87-95
  • MSC: Primary 14K10; Secondary 14D10
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1150646-7
  • MathSciNet review: 1150646