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A linear AFL for quaternion algebras

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  04 March 2025

Nuno Hultberg Open the ORCID record for Nuno Hultberg [Opens in a new window]  and
Andreas Mihatsch Open the ORCID record for Andreas Mihatsch [Opens in a new window]
Nuno Hultberg
Affiliation:
Institute for Theoretical Sciences, Westlake University, 600 Dunyu Rd, Xihu District, Hangzhou, Zhejiang, 310030, P. R. China e-mail: [email protected]
Andreas Mihatsch*
Affiliation:
School of Mathematical Sciences, Zhejiang University, 866 Yuhangtang Rd, Hangzhou, 310058, P. R. China
*
e-mail: [email protected]
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Abstract

We prove new fundamental lemma and arithmetic fundamental lemma identities for general linear groups over quaternion division algebras. In particular, we verify the transfer conjecture and the arithmetic transfer conjecture from Li and Mihatsch (2023, Preprint, arXiv:2307.11716) in cases of Hasse invariant $1/2$.

Keywords

Arithmetic fundamental lemmaquaternion algebraRapoport–Zink spaceorbital integralintersection number

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 14G35: Modular and Shimura varieties
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 23
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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