On saturated distinguished chains over a local field

[摘要] For a separable element alpha over a local field K, we consider a sequence (alpha, alpha(1), ..., alpha(n)) of elements such that alpha(i) is of minimal degree over K with <(upsilon)over bar>(alpha(i-1) - alpha(i)) = sup {<(upsilon)over bar>(alpha(i-1) - beta) \ [K(beta) : K] < [K(alpha(i-1)) : K]} and that alpha(n) belongs to K, where alpha(0) = alpha and <(upsilon)over bar> is the unique valuation on the algebraic closure of K with <(upsilon)over bar>(K-x) = Z. Such a sequence is called a saturated distinguished chain for alpha over K. We study how these chains are determined from alpha and see that these chains are closely related to the ramification of the field K(alpha). (C) 1999 Academic Press.

[发布日期] 1999-12-01