cohomology

(redirected from Cohomology theory)
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cohomology

(ˌkəʊhəˈmɒlədʒɪ)
n
the abstract study of algebraic topology
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It is a particularly timely moment to carry out such a project as the ER has recently developed a new integral p-adic cohomology theory with Bhatt and Scholze, while the Supervisor has recently put Faltings~ machinery on a rigorous base in an extended joint work with Gros.
In this context, a regulator is a map from the algebraic K-theory of an algebraic variety to a suitable cohomology theory such as etale cohomology or Deligne cohomology.
The text begins with basic notions in homotopy theory and introduction to the axioms of generalized cohomology theory.
This result reflects a geometric construction of complex K-theory and suggests that a group theoretic description of a certain cohomology theory for BG might eventually lead to a geometric construction of the cohomology theory.