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Tuitman, Jan. Mathematics of Computation Finite Fields and Their Applications 45 : Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
What is the machinery used? I mean, the integration of complex valued functions of complex variables, or more precisely holomorphic functions, is much a much more interesting topic than measure theory. I have also seen mentioned that Grothendieck's cohomology theories like etale cohomology, crystalline cohomology etc. What could possibly be the connection? The reason for wanting such theories are various. One reason is indicated in George S. One would like to have more analytic ways of thinking about them, and this is one goal of Robert Coleman's theory.
In a recent volume of Asterisque, namely vol. For instance the isomorphism between de Rham cohomology and Betti cohomology involves integrating differential forms over homology classes.
Actually the situation is a bit more intricate; the de Rham cohomology decomposes into various other spaces via the Hodge decomposition.
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