论文标题
关于Kobayashi的Plus/减去规范组和应用的共同学
On the cohomology of Kobayashi's plus/minus norm groups and applications
论文作者
论文摘要
加号和减号组是由Kobayashi构建的，作为具有超大减少的椭圆曲线正式组的子组，它们在Kobayashi对签名的Selmer组的定义中起着重要作用。在本文中，我们研究了这些Plus和减去规范组的共同体。特别是，我们表明这些规范群体在同一个学上是微不足道的。 As an application of our analysis, we establish certain (quasi-)projectivity properties of the non-primitive mixed signed Selmer groups of an elliptic curve with good reduction at all primes above $p$.然后，我们基于这些后一种投影率结果，为签名的Selmer组得出了Kida公式，并研究了签名的Selmer组附加的特征元素的完整性属性。
The plus and minus norm groups are constructed by Kobayashi as subgroups of the formal group of an elliptic curve with supersingular reduction, and they play an important role in Kobayashi's definition of the signed Selmer groups. In this paper, we study the cohomology of these plus and minus norm groups. In particular, we show that these norm groups are cohomologically trivial. As an application of our analysis, we establish certain (quasi-)projectivity properties of the non-primitive mixed signed Selmer groups of an elliptic curve with good reduction at all primes above $p$. We then build on these latter projectivity results to derive a Kida formula for the signed Selmer groups, and study the integrality property of the characteristic element attached to the signed Selmer groups.
