Geometric Applications of the Langlands Correspondence: Reading Rack

This is an annotated reading list for a working seminar at the Institute for Advanced Study during winter/spring 2019. Let me know if you have trouble with any of the links; some of them require access from within Princeton or IAS (possibly via a VPN).

The beginning of the story

The (étale) Langlands correspondence for GL(n)

p-adic Weil cohomology

Bertini-type results over finite fields

Bounding and counting coefficient objects

Newton polygons and p-adic valuations

Étale companions of étale/crystalline coefficients

Vector bundles on curves

Crystalline companions of étale coefficients

Applications of companions