Orthogonal epsilon constants for tame actions of finite groups on surfaces / Darren Glass.

Format:

Book

Manuscript

Microformat

Thesis/Dissertation

Author/Creator:

Glass, Darren, 1969-

Contributor:

Chinburg, Ted, 1954- advisor.

University of Pennsylvania.

Language:

English

Subjects (All):

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Physical Description:

iv, 50 pages ; 29 cm

Production:

2002.

Summary:

In this thesis we suppose G is a finite group acting tamely on a regular projective curve X over Z . Let V be an orthogonal representation of G of dimension 0 and trivial determinant. Our main result determines the sign of the epsilon-constant epsilon( X /G, V) in terms of data associated to the archimedean place and to the crossing points of irreducible components of finite fibers of X , subject to certain standard hypotheses about these fibers. In the course of the proof we associate to V and the action of G on X an element mu( X , G, V) of order two in the Brauer group of Q . Such invariants have been defined by Saito for orthogonal motives of even weight. By contrast, the relevant motive in this paper is ( H1( X ) ⊗ V)G which is symplectic of weight 1.

Notes:

Adviser: Ted Chinburg.

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2002.

Includes bibliographical references.

Local Notes:

University Microfilms order no.: 3043873.

OCLC:

244971562