Journal of Number Theory ( IF 0.6 ) Pub Date : 2018-09-19 , DOI: 10.1016/j.jnt.2018.08.009 James Upton 1
In this paper we consider a tower of number fields arising naturally from a continuous p-adic representation of , referred to as a p-adic Lie tower over K. A recent conjecture of Daqing Wan hypothesizes, for certain p-adic Lie towers of curves over , a stable (polynomial) growth formula for the genus. Here we prove the analogous result in characteristic zero, namely: the p-adic valuation of the discriminant of the extension is given by a polynomial in for i sufficiently large. This generalizes a previously known result on discriminant-growth in -towers of local fields of characteristic zero.
中文翻译:
数域p进李塔的判别稳定性
在本文中,我们考虑一个数字域的塔自然产生于一个连续的p -adic 表示,称为K上的p进李塔。大庆万最近的一个猜想假设,对于某些p -adic Lie towers of curve over,属的稳定(多项式)增长公式。这里我们证明了特征零的类似结果,即:扩展判别式的p进估值由多项式给出因为i足够大。这概括了先前已知的关于判别增长的结果- 特征零的局部场的塔。