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Freeness of Hecke modules at non-minimal levels
- Publication Year :
- 2022
-
Abstract
- We build on the results of [6] to show that the homology groups $\mathrm{H}_{r_1+r_2}(Y_0(\mathcal{N}_\Sigma),\mathcal{O})_{\mathfrak{m}_\Sigma}$ of arithmetic manifolds are free over certain deformation rings $R_\Sigma$, when there are enough geometric characteristic 0 representations. Hitherto we had proved that the homology group has a nonzero free $R_\Sigma$-direct summand. The new ingredient is a commutative algebra argument involving congruence modules defined in higher codimension in [6].<br />Comment: 12 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.13097
- Document Type :
- Working Paper