On a conjecture of Pappas and Rapoport about the standard local model for GL_ d
| Autor: | Alex Weekes, Oded Yacobi, Dinakar Muthiah |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Conjecture Applied Mathematics General Mathematics 010102 general mathematics Structure (category theory) Frobenius splitting Affine Grassmannian (manifold) Type (model theory) 01 natural sciences Scheme (mathematics) 0103 physical sciences 010307 mathematical physics Affine transformation 0101 mathematics Mathematics |
| Zdroj: | Journal für die reine und angewandte Mathematik (Crelles Journal). 2021:175-185 |
| ISSN: | 1435-5345 0075-4102 |
| DOI: | 10.1515/crelle-2020-0030 |
| Popis: | 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 {n\times 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|