Abstract:We introduce and study the notion of ramification ideals in higher ramification theory. After general results on their computation for finite extensions, we discuss their connection with the possibly nontrivial defect of the extensions. We compute them for Artin-Schreier extensions and Kummer extensions of prime degree equal to the residue characteristic, which may or may not have nontrivial defect. We present an example that shows that nontrivial defect in an extension of degree $p^2$, $p$ a prime, may not imply the existence of a nonprincipal ramification ideal.
From: Franz-Viktor Kuhlmann [view email]
[v1]
Mon, 17 Mar 2025 13:30:33 UTC (45 KB)
[v2]
Fri, 25 Apr 2025 07:16:38 UTC (46 KB)
[v3]
Thu, 30 Apr 2026 18:10:16 UTC (29 KB)
[v4]
Sun, 31 May 2026 15:43:55 UTC (29 KB)
[v5]
Wed, 24 Jun 2026 16:36:23 UTC (29 KB)
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