Siegel modulator form (mod p) and algebraic modular forms

In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions ... , where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre's result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) of genus g are the same as the ones given by algebraic modular forms (mod p) on the group GUg(B), as defined in [Gro99] and [Gro98]. The correspondence is obtained by restricting to the superspecial locus of the moduli space of abelian varieties.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Ghitza, Alexandru Edgar, 1976-

Advisor dc:contributor.advisor

• Aise Johan de Jong.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/29346

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29346