# On the Frobenius stable part of Witt vector cohomology

Andre Chatzistamatiou

Number | 15 |
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Author | Andre Chatzistamatiou |

Year | 2010 |

For a proper (not necessarily smooth) variety over a finite field with q elements, Berthelot-Bloch-Esnault proved a trace formula which computes the number of rational points modulo q in terms of the Witt vector cohomology. We show the analogous formula for Witt vector cohomology of finite length. In addition, we prove a vanishing result for the compactly supported \'etale cohomology of a constant p-torsion sheaf on an affine Cohen-Macaulay variety in positive characteristic p.