Absolute de Rham cohomology is a de Rham cohomology theory for arithmetic motives? which provides a spectral interpretation of L-functions. It is viewed as a phenomenon in hypothetical “absolute” geometry “over a field of one element”. It is hoped by some that it may help to approach Riemann hypothesis.
Nagoya conference Witt vectors, foliations, and absolute de Rham cohomology, 2010, participants, schedule
Kedlaya overview slides pdf from Nagoya talk
MathOverflow question Riemann hypothesis via absolute geometry