Poitou–Tate without restrictions on the order
2015; International Press of Boston; Volume: 22; Issue: 6 Linguagem: Inglês
10.4310/mrl.2015.v22.n6.a5
ISSN1945-001X
Autores Tópico(s)Topological and Geometric Data Analysis
ResumoPoitou-Tate without restrictions on the order Kęstutis ČesnavičiusThe Poitou-Tate sequence relates Galois cohomology with restricted ramification of a finite Galois module M over a global field to that of the dual module under the assumption that #M is a unit away from the allowed ramification set.We remove the assumption on #M by proving a generalization that allows arbitrary "ramification sets" that contain the archimedean places.We also prove that restricted products of local cohomologies that appear in the Poitou-Tate sequence may be identified with derived functor cohomology of an adele ring.In our proof of the generalized sequence we adopt this derived functor point of view and exploit properties of a natural topology carried by cohomology of the adeles.2 Cohomology of the adeles as a restricted product 1626 3 Topology on cohomology of the adeles 1641 4 Discreteness of the image of global cohomology inside adelic cohomology 1647 5 Poitou-Tate 1655
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