Geometry of the eigencurve at critical Eisenstein series of weight 2
Geometry of the eigencurve at critical Eisenstein series of weight 2
复制标题
权重为 2 的临界艾森斯坦级数处特征曲线的几何形状
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Dipramit Majumdar
中科院分区：
文献类型：
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作者：
Dipramit Majumdar
In this paper we show that the critical Eisenstein series of weight 2, E_{2}^{crit_{p}}, is smooth in the eigencurve C(l), where l is a prime. We also show that E_{2}^{crit_{p},ord_{l}} is smooth in the full eigencurve C^{full}(l) and E_{2}^{crit_{p},ord_{l_{1}},ord_{l_{2}}} is non-smooth in the full eigencurve C^{full}(l_{1}l_{2}). Further, we show that, E_{2}^{crit_{p}}, is 'etale over the weight space in the eigencurve C(l). As a consequence, we show that level lowering conjecture of Paulin fails to hold at E_{2}^{crit_{p},ord_{l}}.
In this paper we show that the critical Eisenstein series of weight 2, E_{2}^{crit_{p}}, is smooth in the eigencurve C(l), where l is a prime. We also show that E_{2}^{crit_{p},ord_{l}} is smooth in the full eigencurve C^{full}(l) and E_{2}^{crit_{p},ord_{l_{1}},ord_{l_{2}}} is non-smooth in the full eigencurve C^{full}(l_{1}l_{2}). Further, we show that, E_{2}^{crit_{p}}, is 'etale over the weight space in the eigencurve C(l). As a consequence, we show that level lowering conjecture of Paulin fails to hold at E_{2}^{crit_{p},ord_{l}}.