Artin-Schreier extensions and generalized associated orders

作者：Duc Van Huynh^*

来源：Journal of Number Theory, 2014, 136: 28-45.

DOI：10.1016/j.jnt.2013.09.009

• Artin-Schreier extensions
• Associated orders
• Local fields
• Characteristic p
• Akira Aiba
• Galois modules

Let k be the local field F-q((T)), where q is a power of a prime number p. Let L be a totally ramified Artin-Schreier extension of degree p over k and G its Galois group, and let v be a valuation of L such that v(T) = 1. Define M-L(r) = {x is an element of L: v(x) >= r/p}. We give a basis for the O-k-module A(r,b)(L/k) = {x is an element of k[G]: x . M-L(r) subset of M-L(b)}. Moreover, we determine the conditions for which M-L(r) is free over the ring A(r,r).

• 出版日期2014-3