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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.
Breuil, Christophe 1 ; Hellmann, Eugen 1 ; Schraen, Benjamin 1
@article{PMIHES_2019__130__299_0,
author = {Breuil, Christophe and Hellmann, Eugen and Schraen, Benjamin},
title = {A local model for the trianguline variety and applications},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {299--412},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {130},
year = {2019},
doi = {10.1007/s10240-019-00111-y},
mrnumber = {4028517},
zbl = {1454.14120},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00111-y/}
}
TY - JOUR AU - Breuil, Christophe AU - Hellmann, Eugen AU - Schraen, Benjamin TI - A local model for the trianguline variety and applications JO - Publications Mathématiques de l'IHÉS PY - 2019 SP - 299 EP - 412 VL - 130 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00111-y/ DO - 10.1007/s10240-019-00111-y LA - en ID - PMIHES_2019__130__299_0 ER -
%0 Journal Article %A Breuil, Christophe %A Hellmann, Eugen %A Schraen, Benjamin %T A local model for the trianguline variety and applications %J Publications Mathématiques de l'IHÉS %D 2019 %P 299-412 %V 130 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00111-y/ %R 10.1007/s10240-019-00111-y %G en %F PMIHES_2019__130__299_0
Breuil, Christophe; Hellmann, Eugen; Schraen, Benjamin. A local model for the trianguline variety and applications. Publications Mathématiques de l'IHÉS, Tome 130 (2019), pp. 299-412. doi: 10.1007/s10240-019-00111-y
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