A Note on Special Fibers of Shimura Curves and Special Representations

Yih-Jeng Yu

doi:10.11650/tjm/190704

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Home > Journals > Taiwanese J. Math. > Volume 24 > Issue 3 > Article

June, 2020 A Note on Special Fibers of Shimura Curves and Special Representations

Yih-Jeng Yu

Taiwanese J. Math. 24(3): 523-544 (June, 2020). DOI: 10.11650/tjm/190704

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Abstract

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.

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Yih-Jeng Yu. "A Note on Special Fibers of Shimura Curves and Special Representations." Taiwanese J. Math. 24 (3) 523 - 544, June, 2020. https://doi.org/10.11650/tjm/190704

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Received: 29 January 2019; Revised: 25 June 2019; Accepted: 14 July 2019; Published: June, 2020

First available in Project Euclid: 19 May 2020

zbMATH: 07251185

MathSciNet: MR4100707

Digital Object Identifier: 10.11650/tjm/190704

Subjects:

Primary: 11F80 , 11G18 , 14F05 , 14G22 , 14K10

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

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Vol.24 • No. 3 • June, 2020

Mathematical Society of the Republic of China

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Yih-Jeng Yu "A Note on Special Fibers of Shimura Curves and Special Representations," Taiwanese Journal of Mathematics, Taiwanese J. Math. 24(3), 523-544, (June, 2020)

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