We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
SERRE WEIGHTS AND BREUIL'S LATTICE CONJECTURE IN DIMENSION THREE.
- Authors
LE, DANIEL; HUNG, BAO V. LE; LEVIN, BRANDON; MORRA, STEFANO
- Abstract
We prove in generic situations that the lattice in a tame type induced by the completed cohomology of a U(3)-arithmetic manifold is purely local, that is, only depends on the Galois representation at places above p. This is a generalization to GL3 of the lattice conjecture of Breuil. In the process, we also prove the geometric Breuil-M'ezard conjecture for (tamely) potentially crystalline deformation rings with Hodge-Tate weights (2; 1; 0) as well as the Serre weight conjectures of Herzig ['The weight in a Serre-type conjecture for tame n-dimensional Galois representations', Duke Math. J. 149(1) (2009), 37-116] over an unramified field extending the results of Le et al. ['Potentially crystalline deformation 3985 rings and Serre weight conjectures: shapes and shadows', Invent. Math. 212(1) (2018), 1-107]. We also prove results in modular representation theory about lattices in Deligne-Lusztig representations for the group GL3(Fq).
- Subjects
LOGICAL prediction; REPRESENTATION theory; LATTICE theory; DEFORMATION of surfaces; MODULAR groups
- Publication
Forum of Mathematics, Pi, 2020, Vol 8, p1
- ISSN
2050-5086
- Publication type
Article
- DOI
10.1017/fmp.2020.1