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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
12
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Why aren't there more classifying spaces in number theory?
As a topologist, my view is that group cohomology of interest to number theorests seems to generally be with non-trivial module coefficients. Many of the tricks topologists employ to study spaces do …