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Incoherent definite spaces and Shimura varieties. (English) Zbl 1475.11124

Müller, Werner (ed.) et al., Relative trace formulas. Proceedings of the Simons symposium, Schloss Elmau, Germany, April 22–28, 2018. Cham: Springer. Simons Symp., 187-215 (2021).
Summary: In this paper, we define incoherent definite quadratic spaces over totally real number fields and incoherent definite Hermitian spaces over CM fields. We use the neighbors of these spaces to study the local points of orthogonal and unitary Shimura varieties.
For the entire collection see [Zbl 1469.11002].

MSC:

11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14G15 Finite ground fields in algebraic geometry
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References:

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