Taiwanese Journal of Mathematics

A Note on Modularity Lifting Theorems in Higher Weights

Yih-Jeng Yu

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We follow the ideas of Khare and Ramakrishna-Khare and prove the modularity lifting theorem in higher weights. This approach somehow differs from that using Taylor-Wiles systems.

Article information

Taiwanese J. Math., Volume 22, Number 2 (2018), 275-300.

Received: 19 February 2017
Revised: 8 June 2017
Accepted: 11 June 2017
First available in Project Euclid: 8 September 2017

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Zentralblatt MATH identifier

Primary: 11F80: Galois representations 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35] 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]

modularity lifting theorems Hecke algebras Shimura curves vanishing cycles monodromy Galois representations Ramakrishna-Khare systems Čerednik-Drinfel'd uniformizations


Yu, Yih-Jeng. A Note on Modularity Lifting Theorems in Higher Weights. Taiwanese J. Math. 22 (2018), no. 2, 275--300. doi:10.11650/tjm/8147. https://projecteuclid.org/euclid.twjm/1504836034

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