Freeness of Hecke modules at non-minimal levels
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909401503236096 |
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| author | Iyengar, Srikanth B. Khare, Chandrashekhar B. Manning, Jeffrey |
| author_facet | Iyengar, Srikanth B. Khare, Chandrashekhar B. Manning, Jeffrey |
| contents | We build on the results of [6] to show that the homology groups $\mathrm{H}_{r_1+r_2}(Y_0(\mathcal{N}_Σ),\mathcal{O})_{\mathfrak{m}_Σ}$ of arithmetic manifolds are free over certain deformation rings $R_Σ$, when there are enough geometric characteristic 0 representations. Hitherto we had proved that the homology group has a nonzero free $R_Σ$-direct summand. The new ingredient is a commutative algebra argument involving congruence modules defined in higher codimension in [6]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_13097 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Freeness of Hecke modules at non-minimal levels Iyengar, Srikanth B. Khare, Chandrashekhar B. Manning, Jeffrey Number Theory Commutative Algebra 11F80 (primary), 13C10, 13D02 (secondary) We build on the results of [6] to show that the homology groups $\mathrm{H}_{r_1+r_2}(Y_0(\mathcal{N}_Σ),\mathcal{O})_{\mathfrak{m}_Σ}$ of arithmetic manifolds are free over certain deformation rings $R_Σ$, when there are enough geometric characteristic 0 representations. Hitherto we had proved that the homology group has a nonzero free $R_Σ$-direct summand. The new ingredient is a commutative algebra argument involving congruence modules defined in higher codimension in [6]. |
| title | Freeness of Hecke modules at non-minimal levels |
| topic | Number Theory Commutative Algebra 11F80 (primary), 13C10, 13D02 (secondary) |
| url | https://arxiv.org/abs/2208.13097 |