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This article proves, in the case of split groups over arbitrary fields, that all fibers of convolution morphisms attached to parahoric affine flag varieties are paved by products of affine lines and affine lines minus a point. This applies in particular to the affine Grassmannian and to the convolution morphisms in the context of the geometric Satake correspondence. The second part of the article extends these results over $$\mathbb Z$$. Those in turn relate to the recent work of Cass-van den Hove-Scholbach on the geometric Satake equivalence for integral motives, and provide some alternative proofs for some of their results. Comment: 24 pages. Minor error corrected with the addition of Lemma 7.2. Lemma 7.3 added. Material on triviality of morphisms added to section 5. Minor changes in notation. Published version
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The test function conjecture for local models of Weil-restricted groups
We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified) local models attached to all connected reductive groups over $$p$$ -adic local fields with $$p\geqslant 5$$ . In addition, we give a self-contained study of relative affine Grassmannians and loop groups formed using general relative effective Cartier divisors in a relative curve over an arbitrary Noetherian affine scheme.
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- Award ID(s):
- 1801352
- PAR ID:
- 10194811
- Date Published:
- Journal Name:
- Compositio Mathematica
- Volume:
- 156
- Issue:
- 7
- ISSN:
- 0010-437X
- Page Range / eLocation ID:
- 1348 to 1404
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1112/S0010437X20007162
