Franklin

Higher Dimensional Class Field Theory: The variety case [electronic resource].

Author/Creator:
Gruendken, Linda M.
Format/Description:
Book
134 p.
Contained In:
Dissertation Abstracts International 73-06B.

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Subjects:
Mathematics.
Local subjects:
Penn dissertations -- Mathematics. (search)
Mathematics -- Penn dissertations. (search)
System Details:
Mode of access: World Wide Web.
Summary:
Let k be a finite field, and suppose that the arithmetical variety X ⊂ Pnk is an open subset in projective space. Suppose that CX is the Wiesend idele class group of X, pab1 (X) the abelianised fundamental group, and rho X : CX&rarrr;pab 1 (X) the Wiesend reciprocity map. We use the Artin-Schreier-Witt and Kummer Theory of affine k-algebras to prove a full reciprocity law for X. We find necessary and sufficent conditions for a subgroup H < CX to be a norm subgroup: H is a norm subgroup if and only if it is open and its induced covering datum is geometrically bounded. We show that rhoX is injective and has dense image. We obtain a one-to-one correspondence of open geometrically bounded subgroups of CX with open subgroups of pab1 (X). Furthermore, we show that for an etale cover X'' → X with maximal abelian subcover X' → X, the reciprocity morphism induces an isomorphism CX/NCX' ' ≃ Gal(X'/X).
Notes:
Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2011.
Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: .
Adviser: Florian Pop.
Local notes:
School code: 0175.
Contributor:
Pop, Florian, advisor
University of Pennsylvania.
ISBN:
9781267218612
Access Restriction:
Restricted for use by site license.