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 Paul Monsky and Gerard Washnitzer ( 1968), who were motivated by the work of Bernard 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  0865811