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arXiv · 1912.06822

On a conjecture of Pappas and Rapoport about the standard local model for $GL_d$

Dinakar Muthiah·Alex Weekes·Oded Yacobi
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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 $n \times n$ 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.

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Dinakar Muthiah, Alex Weekes, Oded Yacobi. 2019-12-14. On a conjecture of Pappas and Rapoport about the standard local model for $GL_d$. https://arxiv.org/abs/1912.06822

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