Abstract
The capitulation problem concerns the determination of the transfer-kernel Ke((G(L¦k)ab→G(L¦K)ab) for Galois field towers L¦K¦k in certain classformations of number fields. 3 special instances are dealt with: (1) The capitulation kernel can be described in terms of ray knots if L is a ray class field over K. (2) lyanaga's application of the genus conductor is extended to the non-abelian case. (3) The cohomology of the S-idel class group of the maximal extension of k unramified outside a finite set S ⊃ S∞ of primes can be expressed by the cohomology of the S-Leopoldt-kernel. This leads to a description of the respective capitulation kernel and moreover of the Schur multiplier of the Galois group of the maximal p-extension unramified outside p (p≠2) in terms of the usual Leopoldt-kernel.
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Heider, FP. Kapitulationsproblem und knotentheorie. Manuscripta Math 46, 229–272 (1984). https://doi.org/10.1007/BF01185203
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DOI: https://doi.org/10.1007/BF01185203