Talk 14: Weil-Deligne representations and discrete parameters
João Lourenço (Paris 13)

Explain Sections 2.1.4 and 2.1.5. Focus on the following aspects.
(1) Explain the stacks LocWD
LG,F and LocWLG,F and the isomorphism of the former one with LocLG,F . Explain the maps LocLG,F ∼= LocWD LG,F → LocWLG,F → Spf ZLG,F .
(2) Define (essentielly) discrete Langlands parameters (before Def. 2.28 and Def. 2.28 itself).
(3) Explain Prop. 2.32, Cor. 2.33. Mention Lemma 2.34.

Talk 15: The categorical local Langlands conjecture
Timo Richarz (TU Darmstadt)

Recall the theory of (ind)coherent sheaves (Chapter 9). Since we are happy
to restrict to the case that Λ = Q¯ℓ, we may assume that we are in the “classical”
characteristic zero case. Then state the categorical local Langlands conjecture.
Use the opportunity to summarized the first half the seminar.

The final session on February 10 will be a double session from 14:00 to 17:30, followed by dinner.

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