In mathematics, infinitesimal cohomology is a
cohomology theory
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...
for
algebraic varieties
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. ...
introduced by . In characteristic 0 it is essentially the same as
crystalline cohomology
In mathematics, crystalline cohomology is a Weil cohomology theory for schemes ''X'' over a base field ''k''. Its values ''H'n''(''X''/''W'') are modules over the ring ''W'' of Witt vectors over ''k''. It was introduced by and developed by ...
. In nonzero characteristic ''p'' showed that it is closely related to
etale cohomology with mod ''p'' coefficients, a theory known to have undesirable properties.
References
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Algebraic geometry
Cohomology theories
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