On a conjecture of Pappas and Rapoport about the standard local model for GL_ d

Muthiah, D. , Weekes, A. and Yacobi, O. (2020) On a conjecture of Pappas and Rapoport about the standard local model for GL_ d. Journal fur die Reine und Angewandte Mathematik (Crelles Journal), 772, pp. 175-185. (doi: 10.1515/crelle-2020-0030)

Abstract

In their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of n×n matrices. We give a positive answer to their conjecture in full generality. Our main ideas follow naturally from two of our previous works. The first is our proof of a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman on the equations defining type A affine Grassmannians. The second is the work of the first two authors and Kamnitzer on affine Grassmannian slices and their reduced scheme structure. We also present a version of our argument that is almost completely elementary: the only non-elementary ingredient is the Frobenius splitting of Schubert varieties.

• Item Type: Articles
• Additional Information: Dinakar Muthiah was supported by JSPS KAKENHI Grant Number JP19K14495. Alex Weekes was supported in part by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science. Oded Yacobi is supported by the ARC grant DP180102563.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Muthiah, Dr Dinakar
• Authors: Muthiah, D., Weekes, A., and Yacobi, O.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal fur die Reine und Angewandte Mathematik (Crelles Journal)
• Publisher: De Gruyter
• ISSN: 0075-4102
• ISSN (Online): 1435-5345
• Copyright Holders: Copyright © 2021 De Gruyter
• First Published: First published in Journal fur die Reine und Angewandte Mathematik (Crelles Journal) 77:175-185
• Publisher Policy: Reproduced under a Creative Commons License