On Saturated Distinguished Chains over a Local Field

✍ Scribed by Kaori Ota

• Book ID: 102604595
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 257 KB
• Volume: 79
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1999.2437

✦ Synopsis

For a separable element : over a local field K, we consider a sequence (:, : 1 , ..., : n ) of elements such that : i is of minimal degree over K with vÄ (:

and that : n belongs to K, where : 0 =: and vÄ is the unique valuation on the algebraic closure of K with vÄ (K _ )=Z. Such a sequence is called a saturated distinguished chain for : over K. We study how these chains are determined from : and see that these chains are closely related to the ramification of the field K(:).