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