Holmstrom N80 Cohomology and automorphic forms

Maybe I could describe the 7 avatars of the Langlands program.

Things loosely related to Shimura varieties, automorphic forms, and arithmetic groups

Automorphic cohomology

Boundary cohomology

Completed cohomology

Dirac cohomology

l-adic parabolic cohomology

Eisenstein cohomology

Locally analytic cohomology (related to p-adic Langlands, I think)

Parabolic cohomology

Eichler cohomology

Cohomology of arithmetic groups

Overconvergent cohomology

nLab page on N80 Cohomology and automorphic forms