Nekovár duality over p-adic Lie extensions of global fields
Meng Fai Lim
Romyar T. Sharifi
Tate duality is a Pontryagin duality between the th Galois cohomology group of the absolute Galois group of a local field with coefficents in a finite module and the th cohomology group of the Tate twist of the Pontryagin dual of the module. Poitou-Tate duality has a similar formulation, but the duality now takes place between Galois cohomology groups of a global field with restricted ramification and compactly-supported cohomology groups. Nekovár proved analogues of these in which the module in question is a finitely generated module over a complete commutative local Noetherian ring with a commuting Galois action, or a bounded complex thereof, and the Pontryagin dual is replaced with the Grothendieck dual , which is a bounded complex of the same form. The cochain complexes computing the Galois cohomology groups of and are then Grothendieck dual to each other in the derived category of finitely generated -modules. Given a -adic Lie extension of the ground field, we extend these to dualities between Galois cochain complexes of induced modules of and in the derived category of finitely generated modules over the possibly noncommutative Iwasawa algebra with -coefficients.
Cite this article
Meng Fai Lim, Romyar T. Sharifi, Nekovár duality over p-adic Lie extensions of global fields. Doc. Math. 18 (2013), pp. 621–678DOI 10.4171/DM/410