Abstract
We prove an integral
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1404620
Funding statement: The author was supported in part by NSF Grant DMS-1404620.
Acknowledgements
The debt this paper owes to [‘Modularity lifting beyond the Taylor–Wiles method’, preprint 2012, http://arxiv.org/abs/1207.4224] is clear, and the author thanks David Geraghty for many conversations. We thank Mark Kisin for the explaining a proof of Lemma 2.6, and we also thank Brian Conrad for a related proof of the same result in the context of rigid analytic geometry. We thank Toby Gee and Patrick Allen for several useful comments. We also thank Gabor Wiese for the original idea of proving modularity theorems in weight one by working in weight p.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Compatibility of Kisin modules for different uniformizers
- Stably uniform affinoids are sheafy
- Non-minimal modularity lifting in weight one
- Hausdorff theory of dual approximation on planar curves
- Every conformal minimal surface in ℝ3 is isotopic to the real part of a holomorphic\break null curve
- Exotic crossed products and the Baum–Connes conjecture
- Directions in hyperbolic lattices
- Analysis of gauged Witten equation
- The completion problem for equivariant K-theory
Artikel in diesem Heft
- Frontmatter
- Compatibility of Kisin modules for different uniformizers
- Stably uniform affinoids are sheafy
- Non-minimal modularity lifting in weight one
- Hausdorff theory of dual approximation on planar curves
- Every conformal minimal surface in ℝ3 is isotopic to the real part of a holomorphic\break null curve
- Exotic crossed products and the Baum–Connes conjecture
- Directions in hyperbolic lattices
- Analysis of gauged Witten equation
- The completion problem for equivariant K-theory