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The Weil group of a hyper-class formation

Karen Acquista
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Abstract

In the setting of generalized class field theory, one has a field K with a hyper-class formation C, a complex of G_K-modules that plays the role of a class formation. Letting C(L) denote H^0(G_L, C), there is a distinguished cohomology class in H^2(Gal(L/K), C(L)), the hyper-fundamental class. In this paper, we prove that a group extension of Gal(L/K) by C(L) whose corresponding cohomology class is the hyper-fundamental class satisfies the classical axioms of a Weil group.

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Karen Acquista. 2005-08-03. The Weil group of a hyper-class formation. https://arxiv.org/abs/math/0508078

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