Regular integral models for Shimura varieties of orthogonal type. Issue 4 (15th April 2022)

• Record Type: Journal Article
• Authors: Pappas, G.; Zachos, I.
• Is Part Of: Compositio mathematica. Volume 158:Issue 4(2022)
• Page Start: 831
• Page End: 867
• Publication Date: 2022-04-15
• Subjects: 11G18 -- 14G35; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X22007370
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular $p$ -adic integral models for these varieties over odd primes $p$ at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model.