View source for Monsky–Washnitzer cohomology

In [[algebraic geometry]], '''Monsky–Washnitzer cohomology''' is a ''p''-adic [[cohomology theory]] defined for non-singular [[Affine variety|affine varieties]] over [[field (mathematics)|field]]s of positive [[characteristic (algebra)|characteristic]] ''p'' introduced by {{harvs|txt|author1-link=Paul Monsky|last1=Monsky|first1=Paul|last2=Washnitzer|first2=Gerard|author2-link=Gerard Washnitzer|year=1968}}, who were motivated by the work  of {{harvs|txt|last=Dwork|first=Bernard|authorlink=Bernard Dwork|year=1960}}. The idea is to [[lift (mathematics)|lift]] the variety to characteristic 0, and then take a suitable subalgebra of the [[algebraic de Rham cohomology]] of {{harvtxt|Grothendieck|1966}}. The construction was simplified by {{harvtxt|van der Put|1986}}. Its extension to more general varieties is called [[rigid cohomology]].
==References==
*{{Citation | last1=Dwork | first1=Bernard | authorlink=Bernard Dwork| title=On the rationality of the zeta function of an algebraic variety | jstor=2372974 | mr=0140494  | year=1960 | journal=[[American Journal of Mathematics]] | issn=0002-9327 | volume=82 | pages=631–648 | doi=10.2307/2372974}}
* {{Citation | last1=Grothendieck | first1=Alexander | author1-link = Alexander Grothendieck | title=On the de Rham cohomology of algebraic varieties | url=http://www.numdam.org/item?id=PMIHES_1966__29__95_0 | mr=0199194  | year=1966 | journal=Institut des Hautes Études Scientifiques. Publications Mathématiques | issn=0073-8301 | issue=1 | pages=95–103 | doi=10.1007/BF02684807 | volume=29}} (letter to Atiyah, Oct. 14 1963)
*{{Citation | last1=Monsky | first1=P. | last2=Washnitzer | first2=G. | title=Formal cohomology. I | jstor=1970571 | mr=0248141  | year=1968 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=88 | pages=181–217 | doi=10.2307/1970571}}
*{{Citation | last1=Monsky | first1=P. | title=Formal cohomology. II. The cohomology sequence of a pair | jstor=1970572 | mr=0244272  | year=1968 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=88 | pages=218–238 | doi=10.2307/1970572}}
*{{Citation | last1=van der Put | first1=Marius | title=The cohomology of Monsky and Washnitzer | url=http://www.numdam.org/item?id=MSMF_1986_2_23__33_0 | mr=865811  | year=1986 | journal=Mémoires de la Société Mathématique de France|series=Nouvelle Série | issn=0037-9484 | issue=23 | pages=33–59}}
{{DEFAULTSORT:Monsky-Washnitzer cohomology}}
[[Category:Algebraic geometry]]
[[Category:Cohomology theories]]
[[Category:Homological algebra]]