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The heights of formal $ A$-modules

Author: William C. Waterhouse
Journal: Proc. Amer. Math. Soc. 46 (1974), 332-334
MSC: Primary 14L05
MathSciNet review: 0347837
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Abstract: Let $ A$ be a discrete valuation ring, finite over $ {{\mathbf{Z}}_p}$, acting on a commutative formal Lie group of height $ h$. Then $ h$ is a multiple of $ \vert A:{{\mathbf{Z}}_p}\vert$; and if $ A$ acts on the tangent space by scalar multiplications, the dimension of the group is at most $ h/\vert A:{{\mathbf{Z}}_p}\vert$.

References [Enhancements On Off] (What's this?)

  • [1] P. Cartier, Relèvement des groupes formels commutatifs, Séminaire Bourbaki: 1968/69, Exposé 359, Lecture Notes in Math., vol. 179, Springer-Verlag, Berlin and New York, 1971. MR 42 #7460.
  • [2] Michel Demazure, Lectures on 𝑝-divisible groups, Lecture Notes in Mathematics, Vol. 302, Springer-Verlag, Berlin-New York, 1972. MR 0344261
  • [3] Jean Dieudonné, Lie groups and Lie hyperalgebras over a field of characteristic 𝑝>0. IV, Amer. J. Math. 77 (1955), 429–452. MR 0071718,
  • [4] Jonathan Lubin, One-parameter formal Lie groups over 𝔭-adic integer rings, Ann. of Math. (2) 80 (1964), 464–484. MR 0168567,
  • [5] -, Formal $ A$-modules defined over $ A$, Symposia Mathematica, Vol. III (INDAM, Rome, 1968/69), Academic Press, London, 1970, pp. 241-245. MR 42 #260.

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