8 research outputs found
Invariant distributions on p-adic analytic groups
Sei p eine Primzahl, L eine endliche Erweiterung des Körpers Q_p der p-adischen Zahlen, K eine sphärisch vollständige Erweiterung von L und G eine endlich dimensionale, lokal L-analytische Gruppe mit Zentrum Z. In meiner Dissertation leite ich mehrere explizite Beschreibungen des Zentrums der Algebra D(G,K) der lokal analytischen Distributionen auf G mit Werten in K her. Hauptresultat ist die Verallgemeinerung eines Isomorphismus von Harish-Chandra, der für eine reduktive, zerfallende Gruppe das Zentrum von D(G,K) mit der Algebra der Weyl-invarianten, in Z getragenen Distributionen auf einem maximalen Torus von G in Verbindung setzt. Ferner wird die Beziehung zum Bernsteinzentrum der glatten Darstellungstheorie untersucht.Let p be a prime number, L a finite extension of the field Q_p of p-adic
numbers, K a spherically complete extension of L and G a finite
dimensional, locally L-analytic group with center Z. In my thesis I
derive several explicit descriptions of the center of the algebra D(G,K)
of locally analytic distributions on G with values in K. The main
result is a generalization of an isomorphism of Harish-Chandra which in
the case of a split reductive group connects the center of D(G,K) with
the algebra of Weyl-invariant, centrally supported distributions on a
maximal torus of G. Moreover, I study the relation between the center of
D(G,K) and the Bernstein center of smooth representation theory
A quotient of the Lubin-Tate tower II
In this article we construct the quotient M_1/P(K) of the infinite-level
Lubin-Tate space M_1 by the parabolic subgroup P(K) of GL(n,K) of block form
(n-1,1) as a perfectoid space, generalizing results of one of the authors (JL)
to arbitrary n and K/Q_p finite. For this we prove some perfectoidness results
for certain Harris-Taylor Shimura varieties at infinite level. As an
application of the quotient construction we show a vanishing theorem for
Scholze's candidate for the mod p Jacquet-Langlands and the mod p local
Langlands correspondence. An appendix by David Hansen gives a local proof of
perfectoidness of M_1/P(K) when n = 2, and shows that M_1/Q(K) is not
perfectoid for maximal parabolics Q not conjugate to P.Comment: with an appendix by David Hanse
High-performance deep-ultraviolet optics for free-electron lasers
International audienc