Weight elimination in Serre-type conjectures

Abstract

We prove the weight elimination direction of the Serre weight conjectures as formulated by Herzig for forms of $U(n)$ which are compact at infinity and split at places dividing $p$ in generic situations. That is, we show that all modular weights for a mod $p$ Galois representation are contained in the set predicted by Herzig. Under some additional hypotheses, we also show modularity of all the "obvious" weights.

59 pages, v4, minor revision, to appear in Duke Math. Journal

References in corpus (2)

• G-valued local deformation rings and global lifts
• On mod p local-global compatibility for GL_3 in the ordinary case

Cited by in corpus (3)

• Diagrams in the mod $p$ cohomology of Shimura curves
• Serre weight conjectures for $p$-adic unitary groups of rank 2
• Serre weights for three-dimensional wildly ramified Galois representations