The test function conjecture for local models of Weil-restricted groups. (6th July 2020)

• Record Type: Journal Article
• Authors: Haines, Thomas J.; Richarz, Timo
• Is Part Of: Compositio mathematica. Volume 156:Number 7(2020)
• Page Start: 1348
• Page End: 1404
• Publication Date: 2020-07-06
• Subjects: 14G35, -- 11G18, -- 14G10; Shimura varieties, -- local models, -- nearby cycles; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X20007162
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : 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.