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Notes from the Arbeitsgemeinschaft: Geometric Langlands

This page contains notes I took during 2016 Arbeitsgemeinschaft on Geometric Langlands in Oberwolfach. I have edited the notes somewhat, possibly introducing errors.

Here is everything in one file.

Day 1

Adic spaces (Torsten Wedhorn)
Geometric Class Field Theory (Bhargav Bhatt)
The Fargues-Fontaine Curve (Pierre Colmez)
Perfectoid Spaces (Urs Hartl)

Day 2

The Pro-etale and Faithful Topology (Eugen Hellman)
Galois to Automorphic in Geometric Langlands (Tsao-Hsien Chen)
Discussion Session on the Fargues-Fontaine Curve (Gaitsgory, Scholze)
Vector bundles on the Fargues-Fontaine Curve (Gabriel Dospinescu)
Banach-Colmez spaces (Arthur-Cesar Le Bras)

Day 3

The relative Fargues-Fontaine curve (Matthew Morrow)
Beauville-Laszlo uniformization (Yakov Vasharsky)

Day 4

Classification of G-bundles (Michael Rapoport)
Proof of Geometric Langlands for GL(2), I (Stefan Patrikis)
Discussion Session on p-divisible groups (Gaitsgory, Weinstein)
Uniformization of Bun_G (Peter Scholze)
Relation with classical Langlands correspondence (Ana Caraiani)
Discussion Session on constructing the eigensheaf (Gaitsgory)

Day 5

Formulation of Fargues' conjecture (Laurent Fargues)
Proof of Geometric Langlands for GL(2), II (Jochen Heinloth)
Discussion Session on Diamonds (for the perplexed) (Dennis Gaitsgory)
Discussion Session on function-field analogues (Urs Hartl)
The case of G_m (Ulrich Gortz)
Relation with cohomology of Lubin-Tate spaces (Jared Weinstein)