Monsky–Washnitzer cohomology

In algebraic geometry, Monsky–Washnitzer cohomology is a p-adic cohomology theory defined for non-singular affine varieties over fields of positive characteristic p introduced by Monsky and Washnitzer (1968) and Monsky (1968), who were motivated by the work of Dwork (1960). The idea is to lift the variety to characteristic 0, and then take a suitable subalgebra of the algebraic de Rham cohomology of Grothendieck (1966). The construction was simplified by van der Put (1986). Its extension to more general varieties is called rigid cohomology.

References

• Dwork, Bernard (1960), "On the rationality of the zeta function of an algebraic variety", American Journal of Mathematics, 82: 631–648, doi:10.2307/2372974, ISSN 0002-9327, JSTOR 2372974, MR 0140494 
• Grothendieck, Alexander (1966), "On the de Rham cohomology of algebraic varieties", Institut des Hautes Études Scientifiques. Publications Mathématiques, 29 (1): 95–103, doi:10.1007/BF02684807, ISSN 0073-8301, MR 0199194  (letter to Atiyah, Oct. 14 1963)
• Monsky, P.; Washnitzer, G. (1968), "Formal cohomology. I", Annals of Mathematics. Second Series, 88: 181–217, doi:10.2307/1970571, ISSN 0003-486X, JSTOR 1970571, MR 0248141 
• Monsky, P. (1968), "Formal cohomology. II. The cohomology sequence of a pair", Annals of Mathematics. Second Series, 88: 218–238, doi:10.2307/1970572, ISSN 0003-486X, JSTOR 1970572, MR 0244272 
• van der Put, Marius (1986), "The cohomology of Monsky and Washnitzer", Mémoires de la Société Mathématique de France, Nouvelle Série (23): 33–59, ISSN 0037-9484, MR 865811