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- W3100323962 abstract "We describe a model-theoretic setting for the study of Shimura varieties, and study the interaction between model theory and arithmetic geometry in this setting. In particular, we show that the model-theoretic statement of a certain $mathcal{L}_{omega_1, omega}$-sentence having a unique model of cardinality $aleph_1$ is equivalent to a condition regarding certain Galois representations associated with Hodge-generic points. We then show that for modular and Shimura curves this $mathcal{L}_{omega_1, omega}$-sentence has a unique model in every infinite cardinality. In the process, we prove a new characterisation of the special points on any Shimura variety." @default.
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- W3100323962 date "2015-09-30" @default.
- W3100323962 modified "2023-09-26" @default.
- W3100323962 title "CATEGORICITY OF MODULAR AND SHIMURA CURVES" @default.
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