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Results tagged with algebraic-number-theory
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user 3208
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
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Does this exact sequence split?
Let $K$ be a number field. $O_K$ be its ring of integers, so $O_K^*$ are the units.
We have sequence
$1 \rightarrow O_K^* \rightarrow K^* \rightarrow K^*/O_K^* \rightarrow 1$
Note that $K^*/O_K^*$ is …
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