Higgs cohomology, p-curvature, and the Cartier operator <br> <p>

Arthur Ogus (UC Berkeley) <br><p>

We give a generalization of the Cartier isomorphism, calculating <br>
the De Rham cohomology sheaves of an arbitrary module with integrable <br>
connection in characterstic p.  The answer is expressed in terms <br>
of the Higgs complex defined by the p-curvature of the connection. <br>