Siegel modulator form (mod p) and algebraic modular forms
Author(s)Ghitza, Alexandru Edgar, 1976-
Massachusetts Institute of Technology. Dept. of Mathematics.
Aise Johan de Jong.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.Includes bibliographical references (p. 101-104) and index.
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology