Representations of fundamental groups of abelian varieties in characteristic p / Brett Frankel.

Format:

Book

Manuscript

Thesis/Dissertation

Author/Creator:

Frankel, Brett, author.

Contributor:

Chinburg, Ted, 1954- degree supervisor, degree committee member.

Haglund, James, degree committee member.

Harbater, David, degree committee member.

University of Pennsylvania. Department of Mathematics, degree granting institution.

Language:

English

Subjects (All):

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Physical Description:

vi, 31 leaves ; 29 cm

Production:

[Philadelphia, Pennsylvania] : University of Pennsylvania, 2016.

Summary:

Let Ag be an abelian variety of dimension g and p-rank [lambda] [less than or equal to] 1 over an algebraically closed field of characteristic p > 0 . We compute the number of homomorphisms from [pi]1 ét (Ag) to GLn(Fq), where q is any power of p. We show that for fixed g, [lambda], and n, the number of such representations is polynomial in q. We show that the set of such homomorphisms forms a constructable set, and use the geometry of this space to deduce information about the coefficients and degree of the polynomial. In the last chapter we prove a divisibility theorem about the number of homomorphisms from certain semidirect products of profinite groups into finite groups.

Notes:

Ph. D. University of Pennsylvania 2016.

Department: Mathematics.

Supervisor: Ted Chinburg.

Includes bibliographical references.

OCLC:

961021932