Monsky–Washnitzer cohomology
From HandWiki
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
- 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, http://www.numdam.org/item?id=PMIHES_1966__29__95_0 (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
- 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
- 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, http://www.numdam.org/item?id=MSMF_1986_2_23__33_0
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