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The equivariant
Tamagawa number conjectures for modular motives with
coefficients in Hecke algebras
Olivier Fouquet |
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Vol. 7 (2025), No. 3-4, 791–829
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Abstract |
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Modular motives have coefficients in Hecke algebras. According to the equivariant philosophy, special values of -functions of eigencuspforms should therefore exhibit equivariant properties with respect to various Hecke actions. This article shows that this is indeed the case at least under broad conditions on ramification and deduces from them new properties of the Iwasawa main conjecture for modular forms. |
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Dedicated to the memory of Joël Bellaïche |
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Keywords
modular forms, Iwasawa theory, Tamagawa number conjectures
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Mathematical Subject Classification
Primary: 11F03, 11F80, 11G40, 11M41, 11R23
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Milestones
Received: 19 January 2024
Revised: 21 December 2024
Accepted: 5 January 2025
Published: 12 September 2025
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Authors |
| Olivier Fouquet | |
| Laboratoire de mathématiques de
Besançon Université Marie et Louis Pasteur Besançon France |
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| © 2025 MSP (Mathematical Sciences Publishers). |
