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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Symmetric nilpotent matrices with maximal rank and a conjecture of Grothendieck-Koblitz

Author: Ching-Li Chai
Journal: Proc. Amer. Math. Soc. 119 (1993), 87-95
MSC: Primary 14K10; Secondary 14D10
MathSciNet review: 1150646
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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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PII: S 0002-9939(1993)1150646-7
Article copyright: © Copyright 1993 American Mathematical Society