A local model for the triangulate variety and applications

Hellmann, Eugen

Forschungsartikel (Zeitschrift) | Peer reviewed

Zusammenfassung

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 eigenvari- eties

Details zur Publikation

FachzeitschriftPublications Mathématiques de L'IHÉS (Publ. Math. Inst. Hautes Etudes Sci.)
Jahrgang / Bandnr. / Volume130
Seitenbereich229-412
StatusVeröffentlicht
Veröffentlichungsjahr2019
Sprache, in der die Publikation verfasst istEnglisch
StichwörterA local model for the triangulate variety and applications

Autor*innen der Universität Münster

Hellmann, Eugen
Professur für Theoretische Mathematik (Prof. Hellmann)