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Results tagged with algebraic-number-theory
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user 97316
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
1
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What else does the Tate-Nakayama lemma tell us about class field theory?
I don't know the answer to your question in all generality. However, if one continues with $M=\mathbb{Z}$ and $C=C_K$ then one can ask what happens as we vary $i$.
for $i=-3$ we identify $H^{-3}(C, \ …
- 953
4
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Explicit invariant map in local class field theory
Let $K$ be a $p$-adic field with algebraic closure $\overline{K}$. Then if $K^\text{nr}$ is the maximal unramified extension of $K$ in $\overline{K}$, there is an explicit invariant map:
$$
H^2(\Gamma …
- 953