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arXiv · 2208.13097

Freeness of Hecke modules at non-minimal levels

Srikanth B. Iyengar·Chandrashekhar B. Khare·Jeffrey Manning
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Abstract

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].

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Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning. 2022-08-27. Freeness of Hecke modules at non-minimal levels. https://arxiv.org/abs/2208.13097

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