Taiwanese Journal of Mathematics

A Note on Special Fibers of Shimura Curves and Special Representations

Yih-Jeng Yu

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We study the geometry of the special fibers of certain Shimura curves and give a direct proof of global-to-local Jacquet-Langlands compatibility by Čerednik-Drinfel'd uniformizations theorem.

Article information

Taiwanese J. Math., Volume 24, Number 3 (2020), 523-544.

Received: 29 January 2019
Revised: 25 June 2019
Accepted: 14 July 2019
First available in Project Euclid: 19 May 2020

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Primary: 11F80: Galois representations 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35] 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14G22: Rigid analytic geometry 14K10: Algebraic moduli, classification [See also 11G15]

Shimura curves vanishing cycles Galois representations Čerednik-Drinfel'd uniformizations


Yu, Yih-Jeng. A Note on Special Fibers of Shimura Curves and Special Representations. Taiwanese J. Math. 24 (2020), no. 3, 523--544. doi:10.11650/tjm/190704. https://projecteuclid.org/euclid.twjm/1589875217

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