Class groups and local indecomposability for non-CM forms
| العنوان: | Class groups and local indecomposability for non-CM forms |
|---|---|
| المؤلفون: | Carl Wang-Erickson, Haruzo Hida, Francesc Castella |
| المصدر: | Journal of the European Mathematical Society |
| بيانات النشر: | European Mathematical Society - EMS - Publishing House GmbH, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Class (set theory), Pure mathematics, 11F80, Property (philosophy), Mathematics - Number Theory, Group (mathematics), Mathematics::Number Theory, Applied Mathematics, General Mathematics, 010102 general mathematics, Deformation theory, Complex multiplication, 16. Peace & justice, Indecomposability, Galois module, 01 natural sciences, math.NT, 11F80 (11F33, 11R23), FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Mathematics |
| الوصف: | In the late 1990's, R. Coleman and R. Greenberg (independently) asked for a global property characterizing those $p$-ordinary cuspidal eigenforms whose associated Galois representation becomes decomposable upon restriction to a decomposition group at $p$. It is expected that such $p$-ordinary eigenforms are precisely those with complex multiplication. In this paper, we study Coleman-Greenberg's question using Galois deformation theory. In particular, for $p$-ordinary eigenforms which are congruent to one with complex multiplication, we prove that the conjectured answer follows from the $p$-indivisibility of a certain class group. Comment: 40 pages, with a 11-page appendix by Haruzo Hida. v3: improvements to exposition, minor corrections |
| تدمد: | 1435-9855 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1a43c6bb7f1915b82a544d9abb3b47cc https://doi.org/10.4171/jems/1107 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....1a43c6bb7f1915b82a544d9abb3b47cc |
| قاعدة البيانات: | OpenAIRE |
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