2008/11/30 by Joachim Mahnkopf, Mahnkopf, Joachim
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.0812.0179
openalex publication_date 2008/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this preprint we prove that any finite slope modular form fits into a p-adic family of modular forms which is indexed by the weight. Here, the term p-adic family means that p-adic congruences between weights entail certain p-adic congruences between the corresponding modular forms. We also show that the dimension of the slope subspace of the space of modular forms does not depend on the weight. Both statements are predicted by the Mazur-Gouvea Conjecture, which has been proven by Coleman using methods from rigid analytic geometry. In contrast our proof is based on a comparison of (topological) trace formulas.