On the abelian groups which occur as Galois cohomology groups of global unit groups
Manabu Ozaki

TL;DR
This paper characterizes which abelian groups appear as Galois cohomology groups of global unit groups in unramified G-extensions of number fields, focusing on finite p-groups for specific cohomological degrees.
Contribution
It determines the sets of possible Galois cohomology groups for degrees 0, 1, 2, and 4 when G is a finite p-group, providing new classifications.
Findings
Identifies all isomorphism classes of Galois cohomology groups for specified degrees.
Provides explicit descriptions for p-group cases.
Advances understanding of the structure of global units in Galois extensions.
Abstract
For any finite group G and integer i, let be the set of all the isomorphism classes of the Galois cohomology groups , where K/k runs over all the unramified G-extension of number fields and E_K denotes the global unit group of K. We will determine for i=0,1,2, and 4 in the case where G is a finite p-group.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology
