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mazur’s inequality

Journal of the Institute of Mathematics of Jussieu (1)

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A CONVERSE TO MAZUR’S INEQUALITY FOR SPLIT CLASSICAL GROUPS
Catherine Lucarelli
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 3 / Issue 2 / April 2004

Published online by Cambridge University Press:

28 April 2004, pp. 165-183

Print publication:

April 2004
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Given a lattice in an isocrystal, Mazur’s inequality states that the Newton point of the isocrystal is less than or equal to the invariant measuring the relative position of the lattice and its transform under Frobenius. Conversely, it is known that any potential invariant allowed by Mazur’s inequality actually arises from some lattice. These can be regarded as statements about the group $GL_n$. This paper proves an analogous converse theorem for all split classical groups.
AMS 2000 Mathematics subject classification: Primary 14L05. Secondary 11S25; 14F30; 20G25