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Creators/Authors contains: "Thorne, Jack"

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  1. ; ; ; ; (, Compositio Mathematica)
    Let$$G$$be a split semisimple group over a global function field$$K$$. Given a cuspidal automorphic representation$$\Pi$$of$$G$$satisfying a technical hypothesis, we prove that for almost all primes$$\ell$$, there is a cyclic base change lifting of$$\Pi$$along any$$\mathbb {Z}/\ell \mathbb {Z}$$-extension of$$K$$. Our proof does not rely on any trace formulas; instead it is based on using modularity lifting theorems, together with a Smith theory argument, to obtain base change for residual representations. As an application, we also prove that for any split semisimple group$$G$$over a local function field$$F$$, and almost all primes$$\ell$$, any irreducible admissible representation of$$G(F)$$admits a base change along any$$\mathbb {Z}/\ell \mathbb {Z}$$-extension of$$F$$. Finally, we characterize local base change more explicitly for a class of toral representations considered in work of Chan and Oi. 
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  2. ; (, Forum of Mathematics, Sigma)
    Abstract Let F be a CM number field. We generalise existing automorphy lifting theorems for regular residually irreducible p -adic Galois representations over F by relaxing the big image assumption on the residual representation. 
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  3. ; ; (, Annales scientifiques de l'École Normale Supérieure)
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  4. ; ; ; ; ; ; ; ; ; (, Annals of Mathematics)
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  5. ; ; ; (, Acta Mathematica)
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