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Discriminant-stability in p-adic Lie towers of number fields
Journal of Number Theory ( IF 0.6 ) Pub Date : 2018-09-19 , DOI: 10.1016/j.jnt.2018.08.009
James Upton 1
Affiliation  

In this paper we consider a tower of number fields K(1)K(0)K arising naturally from a continuous p-adic representation of Gal(Q¯/K), 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 Fp, 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 K(i)/K is given by a polynomial in i,pi for i sufficiently large. This generalizes a previously known result on discriminant-growth in Zp-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ķ(1)ķ(0)ķ自然产生于一个连续的p -adic 表示加尔(¯/ķ),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 overFp,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ķ(一世)/ķ由多项式给出一世,p一世因为i足够大。这概括了先前已知的关于判别增长的结果Zp- 特征零的局部场的塔。

更新日期:2018-09-19
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