Generalizes Breuil-Hellmann-Schraen theorem to show smoothness and normality of trianguline variety for split reductive groups and proves crystallinity criterion for G-structured (ϕ,Γ_K)-modules.
Families of trianguline representations and finite slope spaces
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abstract
We apply the theory of families of (phi,Gamma)-modules to trianguline families as defined by Chenevier. This yields a new definition of Kisin's finite slope subspace as well as higher dimensional analogues. Especially we show that these finite slope spaces contain eigenvarieties for unitary groups as closed subspaces. This implies that the representations arising from overconvergent p-adic automorphic forms on certain unitary groups are trianguline when restricted to the local Galois group.
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math.NT 1years
2026 1verdicts
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The trianguline variety for reductive groups
Generalizes Breuil-Hellmann-Schraen theorem to show smoothness and normality of trianguline variety for split reductive groups and proves crystallinity criterion for G-structured (ϕ,Γ_K)-modules.