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arXiv · 1411.7260

Une interpr\'etation modulaire de la vari\'et\'e trianguline

Christophe Breuil·Eugen Hellmann·Benjamin Schraen
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Abstract

Using a patching module constructed in recent work of Caraiani, Emerton, Gee, Geraghty, Pa{\v{s}}k{\=u}nas and Shin we construct some kind of analogue of an eigenvariety. We can show that this patched eigenvariety agrees with a union of irreducible components of a space of trianguline Galois representations. Building on this we discuss the relation with the modularity conjectures for the crystalline case, a conjecture of Breuil on the locally analytic socle of representations occurring in completed cohomology and with a conjecture of Bella\"iche and Chenevier on the complete local ring at certain points of eigenvarieties.

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Christophe Breuil, Eugen Hellmann, Benjamin Schraen. 2014-11-26. Une interpr\'etation modulaire de la vari\'et\'e trianguline. https://doi.org/10.1007/s00208-016-1422-1

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