论文标题
Bergdall-Pollack的幽灵猜想的当地类似物
A local analogue of the ghost conjecture of Bergdall-Pollack
论文作者
论文摘要
我们制定了Bergdall和Pollack的幽灵猜想的局部类似物，这基本上纯粹依赖于GL_2（Q_P）的表示理论。我们进一步研究了幽灵系列及其牛顿多边形的组合特性，尤其是对牛顿多边形的顶点的表征，并证明了斜坡的完整性结果。在即将进行的续集中，我们将在一些轻度假设下证明这种局部幽灵的猜想，并提供算术应用。
We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of GL_2(Q_p). We further study the combinatorial properties of the ghost series as well as its Newton polygon, in particular, giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes. In a forthcoming sequel, we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications.
