Lifting Elementary Abelian Covers of Curves / Jianing Yang.

Format:

Book

Thesis/Dissertation

Author/Creator:

Yang, Jianing, author.

Contributor:

University of Pennsylvania. Mathematics, degree granting institution.

Language:

English

Subjects (All):

Mathematics.

Applied mathematics.

Mathematics--Penn dissertations.

Penn dissertations--Mathematics.

Local Subjects:

Mathematics.

Applied mathematics.

Mathematics--Penn dissertations.

Penn dissertations--Mathematics.

Physical Description:

1 online resource (59 pages)

Distribution:

Ann Arbor : ProQuest Dissertations & Theses, 2023

Contained In:

Dissertations Abstracts International 84-12B.

Place of Publication:

[Philadelphia, Pennsylvania] : University of Pennsylvania, 2022.

Language Note:

English

Summary:

Given a Galois cover of curves f over a field of characteristic p, the lifting problem asks whether there exists a Galois cover over a complete mixed characteristic discrete valuation ring whose reduction is f . In this thesis, we try to answer this question in the case where the Galois groups are elementary abelian p-groups. We prove a combinatorial criterion for lifting an elementary abelian p-cover, dependent on the branch loci of its p-cyclic subcovers. Moreover, we study how branch points of a lift coalesce on the special fiber. Finally, we construct lifts for several families of (\uD835\uDD6B/2)3-covers of various conductor types, both with equidistant branch locus geometry and non-equidistant branch locus geometry.

Notes:

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

Advisors: Harbater, David; Committee members: Haglund, James; Hartmann, Julia.

Department: Mathematics.

Ph.D. University of Pennsylvania 2023.

Local Notes:

School code: 0175

ISBN:

9798379751142

Access Restriction:

Restricted for use by site license.