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Publications mathématiques de l'IHÉS

, Volume 130, Issue 1, pp 299–412 | Cite as

A local model for the trianguline variety and applications

  • Christophe BreuilEmail author
  • Eugen Hellmann
  • Benjamin Schraen
Article
  • 49 Downloads

Abstract

We describe the completed local rings of the trianguline variety at certain points of integral weights in terms of completed local rings of algebraic varieties related to Grothendieck’s simultaneous resolution of singularities. We derive several local consequences at these points for the trianguline variety: local irreducibility, description of all local companion points in the crystalline case, combinatorial description of the completed local rings of the fiber over the weight map, etc. Combined with the patched Hecke eigenvariety (under the usual Taylor-Wiles assumptions), these results in turn have several global consequences: classicality of crystalline strictly dominant points on global Hecke eigenvarieties, existence of all expected companion constituents in the completed cohomology, existence of singularities on global Hecke eigenvarieties.

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Copyright information

© IHES and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Christophe Breuil
    • 1
    Email author
  • Eugen Hellmann
    • 2
  • Benjamin Schraen
    • 3
  1. 1.C.N.R.S., Laboratoire de Mathématique d’Orsay, Université Paris-SudUniversité Paris-SaclayOrsayFrance
  2. 2.Mathematisches InstitutUniversität MünsterMünsterGermany
  3. 3.Laboratoire de Mathématique d’Orsay, Université Paris-SudUniversité Paris-SaclayOrsayFrance

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