Geodesic
SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE
Forum of Mathematics, Pi, Tome 8 (2020)

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\text{GL}_{3}$ of the lattice conjecture of Breuil. In the process, we also prove the geometric Breuil–Mézard 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 $\text{GL}_{3}(\mathbb{F}_{q})$. 
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     author = {DANIEL LE and BAO V. LE HUNG and BRANDON LEVIN and STEFANO MORRA},
     title = {SERRE {WEIGHTS} {AND} {BREUIL{\textquoteright}S} {LATTICE} {CONJECTURE} {IN} {DIMENSION} {THREE}},
     journal = {Forum of Mathematics, Pi},
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DANIEL LE; BAO V. LE HUNG; BRANDON LEVIN; STEFANO MORRA. SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE. Forum of Mathematics, Pi, Tome 8 (2020). doi: 10.1017/fmp.2020.1

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