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Galois co-descent for étale wild kernels and capitulation

Manfred Kolster, Abbas Movahhedi (2000)

Annales de l'institut Fourier

Let F be a number field with ring of integers o F . For a fixed prime number p and i 2 the étale wild kernels W K 2 i - 2 e ´ t ( F ) are defined as kernels of certain localization maps on the i -fold twist of the p -adic étale cohomology groups of spec o F [ 1 p ] . These groups are finite and coincide for i = 2 with the p -part of the classical wild kernel W K 2 ( F ) . They play a role similar to the p -part of the p -class group of F . For class groups, Galois co-descent in a cyclic extension L / F is described by the ambiguous class formula given by genus theory....

Galois groups of tamely ramified p -extensions

Nigel Boston (2007)

Journal de Théorie des Nombres de Bordeaux

Very little is known regarding the Galois group of the maximal p -extension unramified outside a finite set of primes S of a number field in the case that the primes above p are not in S . We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.

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