论文标题
Hecke模块在非最小程度上
Freeness of Hecke modules at non-minimal levels
论文作者
论文摘要
我们基于[6]的结果，以表明同源组$ \ mathrm {h} _ {r_1+r_2}（y_0（y_0（\ mathcal {n}_σ），\ mathcal {o} _}）几何特性0表示。迄今为止，我们已经证明了同源组具有非零的免费$r_σ$ - 直接求和。新成分是一个涉及[6]中较高编码中定义的一致性模块的交换代数参数。
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].
