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arXiv · 2108.02823

Modularity of trianguline Galois representations

Rebecca Bellovin
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Abstract

We use the theory of trianguline $(\varphi,\Gamma)$-modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at $p$, including those with characteristic $p$ coefficients. The use of pseudorigid spaces lets us construct integral models of the trianguline varieties of [BHS17b], [Che13] after bounding the slope, and we carry out a Taylor--Wiles patching argument for families of overconvergent modular forms. This permits us to construct a patched quaternionic eigenvariety and deduce our modularity results.

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Rebecca Bellovin. 2021-08-05. Modularity of trianguline Galois representations. https://arxiv.org/abs/2108.02823

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