On families of weakly admissible filtered phi-modules and the adjoint quotient of ${GL}_d$

Eugen Hellmann

doi:10.4171/dm/358

JournalsdmVol. 16pp. 969–991

On families of weakly admissible filtered phi-modules and the adjoint quotient of $G L_{d}$

Eugen Hellmann
Mathematisches Institut der Universität Bonn Endenicher Allee 60 53115 Bonn Germany

$On families of weakly admissible filtered phi-modules and the adjoint quotient of ${GL}_d$ cover$

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Abstract

We study the relation of the notion of weak admissibility in families of filtered $ϕ$ -modules, as considered in [He], with the adjoint quotient. We show that the weakly admissible subset is an open subvariety in the fibers over the adjoint quotient. Further we determine the image of the weakly admissible set in the adjoint quotient generalizing earlier work of Breuil and Schneider.

Cite this article

Eugen Hellmann, On families of weakly admissible filtered phi-modules and the adjoint quotient of $G L_{d}$ . Doc. Math. 16 (2011), pp. 969–991

DOI 10.4171/DM/358