**Title:** On mod p local-global compatibility for GL_3 in the ordinary case

**Speaker:** Stefano Morra

**Speaker Info:** Toronto

**Brief Description:**

**Special Note**:

**Abstract:**

Let \rho : G_{\Q_p} \rightarrow GL_3(F_p) be a maximally nonsplit, ordinary Galois representation. If \rho is Fontaine-Laffaille and sufficiently generic, the \phi-action on the associated Fontaine-Laffaille module lets us detect a local Galois invariant. On the other hand, let \pi be a smooth GL_3(\Q_p)-representation over F_p. If \pi verifies appropriate conditions with respect to its pro-p Iwahori invariants, the action of carefully chosen group algebra operators lets us detect a local automorphic invariant. The talk is aimed at showing that, in a global situation and under appropriate modularity conditions, the two invariants coincide.This is joint work with Florian Herzig at Toronto.

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