A quotient of the LubinTate tower II
Abstract
In this article we construct the quotient M_1/P(K) of the infinitelevel LubinTate space M_1 by the parabolic subgroup P(K) of GL(n,K) of block form (n1,1) 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 HarrisTaylor 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 JacquetLanglands 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 arXiv:
 arXiv:1812.08203
 Bibcode:
 2018arXiv181208203J
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14G35;
 14G22;
 11S37
 EPrint:
 final version, accepted for publication in Mathematische Annalen