The Hecke Algebra T_k has Large Index

2003/11/21 by Frank Calegari, Calegari, Frank, Matthew Emerton +1
Mathematics · #11F11 #11F80 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F80

paper · pdf · doi:10.48550/arxiv.math/0311367

13 pages, to appear in Math Research Letters

arxiv created 2003/11/21 · openalex publication_date 2003/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T_k denote the Hecke algebra acting on newforms of weight k and level N. We prove that the power of p dividing the index of T_k inside its normalisation grows at least linearly with k (for fixed N), answering a question of Serre. We also apply our method to give heuristic evidence towards recent conjectures of Buzzard and Mazur.

Citations

• Limites de représentations cristallines

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