Explicit computations in Iwasawa theory

We give two algorithms to compute layers of the anticyclotomic \({\bf Z}_3\)-extension of an imaginary quadratic field. The first is based on complex multiplication techniques for nonmaximal orders; the second is based on Kummer theory. As an illustration of our results, we use the mirroring princip...

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Hauptverfasser: Broker, Reinier, Hubbard, David, Washington, Lawrence C
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description We give two algorithms to compute layers of the anticyclotomic \({\bf Z}_3\)-extension of an imaginary quadratic field. The first is based on complex multiplication techniques for nonmaximal orders; the second is based on Kummer theory. As an illustration of our results, we use the mirroring principle to derive results on the structure of class groups of nonmaximal orders.
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subjects Algorithms
Fields (mathematics)
Mathematics - Number Theory
Number theory
title Explicit computations in Iwasawa theory
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