On a conjecture of Pappas and Rapoport about the standard local model\n for $GL_d$ Article Swipe
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· 2019
· Open Access
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· DOI: https://doi.org/10.48550/arxiv.1912.06822
· OA: W4287994045
In their study of local models of Shimura varieties for totally ramified\nextensions, Pappas and Rapoport posed a conjecture about the reducedness of a\ncertain subscheme of $n \\times n$ matrices. We give a positive answer to their\nconjecture in full generality. Our main ideas follow naturally from two of our\nprevious works. The first is our proof of a conjecture of Kreiman, Lakshmibai,\nMagyar, and Weyman on the equations defining type A affine Grassmannians. The\nsecond is the work of the first two authors and Kamnitzer on affine\nGrassmannian slices and their reduced scheme structure. We also present a\nversion of our argument that is almost completely elementary: the only\nnon-elementary ingredient is the Frobenius splitting of Schubert varieties.\n
