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A converse to Mazur’s inequality for split classical groups. (English) Zbl 1054.14059
Summary: 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 \(GL_n\). The author proves an analogous converse theorem for all split classical groups.

MSC:
14L05 Formal groups, \(p\)-divisible groups
11S25 Galois cohomology
14F30 \(p\)-adic cohomology, crystalline cohomology
20G25 Linear algebraic groups over local fields and their integers
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