On the splitting of the exact sequence, relating the wild and tame kernels

Luca Caputo (1) , Abbas C. Movahhedi (1)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information

Let k be a number field. For an odd prime p and an integer i>1, the i-th \'etale wild kernel is contained in the second cohomology group of o'_k with coefficients in Zp(i), where o'_k is the ring of p-integers of k. Using Iwasawa theory, we give conditions for this inclusion to split. In particular we relate this splitting problem to the triviality of two invariants, namely the asymptotic kernels of the Galois descent and codescent for class groups along the cyclotomic tower of k. We illustrate our results in both split and non-split cases for quadratic number fields

Domaines: Théorie des nombres [math.NT]

Luca Caputo, Abbas C. Movahhedi. On the splitting of the exact sequence, relating the wild and tame kernels. Journal of Pure and Applied Algebra, 2015, 219 (9), pp.3701-3720. ⟨10.1016/j.jpaa.2014.12.018⟩. ⟨hal-01314997⟩