Indices of inseparability and refined ramification breaks

Indices of inseparability for elementary abelian p-extensions

Let K be a local field whose residue field is a finite field of characteristic p, and let L/K be a finite totally ramified Galois extension. Fried and Heiermann defined the "indices of inseparability" of L/K, a refinement of the ramification data of L/K. We give a method for computing the indices of inseparability of the extension L/K in terms of the norm group N_{L/K}(L^*) in the case where K has characteristic p and Gal(L/K) is an elementary abelian p-group with a single ramification break. In some cases our methods lead to simple formulas for the indices of inseparability.

Indices of inseparability in towers of field extensions

Let $K$ be a local field whose residue field has characteristic $p$ and let $L/K$ be a finite separable totally ramified extension of degree $n=ap^ν$. The indices of inseparability $i_0,i_1,...,i_ν$ of $L/K$ were defined by Fried in the case char$(K)=p$ and by Heiermann in the case char$(K)=0$; they give a refinement of the usual ramification data for $L/K$. The indices of inseparability can be used to construct "generalized Hasse-Herbrand functions" $ϕ_{L/K}^j$ for $0\le j\leν$. In this paper we give an interpretation of the values $ϕ_{L/K}^j(c)$ for natural numbers $c$. We use this interpret…

Refined ramification breaks in characteristic $p$

Let $K$ be a local field of characteristic $p$ and let $L/K$ be a totally ramified elementary abelian $p$-extension with a single ramification break $b$. Byott and Elder defined the refined ramification breaks of $L/K$, an extension of the usual ramification data. In this paper we give an alternative definition for the refined ramification breaks, and we use Artin-Schreier theory to compute both versions of the breaks in some special cases.

关于新分歧断裂的必要性

On the necessity of new ramification breaks

分支不变量对于确定局部域扩张中理想的伽罗瓦模结构是必要的，但一般来说不是充分的。这种不足与初等阿贝尔扩张有关，在初等阿贝尔扩张中，人们可以定义一个细化的分歧过滤--一个具有更多分歧断裂的过滤[JNTB 17（2005）]。第一个细化的断裂数来自于通常的分歧过滤，因此是必要的。在这里，我们研究第二个细化的休息数。

On refined metric and hermitian structures in arithmetic, I: Galois-Gauss sums and weak ramification

We use techniques of relative algebraic K-theory to develop a common refinement of the existing theories of metrized and hermitian Galois structures in arithmetic. As a first application of this very general approach, we then use it to prove several new results, and to formulate a framework of new conjectures, concerning the detailed arithmetic properties of wildly ramified Galois-Gauss sums.

关于四元数扩张中的野分歧

On wild ramification in quaternion extensions

四元数扩展通常是表现出特殊性质的最小扩展。例如，在Hasse-Arf定理的设定中，四元数扩展被用来说明上分支数不需要是整数的事实。这些扩展在伽罗瓦模结构中起着类似的作用。为了更好地理解这些例子，我们目录的分歧过滤，可能在完全分歧的扩展并矢数域。有趣的是，我们发现，目录依赖于，尖锐的下界，在细化的分歧过滤，这是与双四次子域。此外，这些例子，作为哈塞-阿尔夫结论的反例，只有当精细过滤以两种不同的方式极端时才出现。