dc.contributor.author | Byott, NP | |
dc.contributor.author | Childs, LN | |
dc.contributor.author | Elder, GG | |
dc.date.accessioned | 2017-07-26T08:28:03Z | |
dc.date.issued | 2018-06-01 | |
dc.description.abstract | Let L/K be a finite, totally ramified p-extension of complete local fields with residue fields of characteristic p > 0, and let A be a K-algebra acting on L. We define the concept of an A-scaffold on L, thereby extending and refining the notion of a Galois scaffold considered in several previous papers, where L/K was Galois and A = K[G] for G = Gal(L/K). When a suitable A-scaffold exists, we show how to answer questions generalizing those of classical integral Galois module theory. We give a necessary and sufficient condition, involving only numerical parameters, for a given fractional ideal to be free over its associated order in A. We also show how to determine the number of generators required when it is not free, along with the embedding dimension of the associated order. In the Galois case, the numerical parameters are the ramification breaks associated with L/K. We apply these results to biquadratic Galois extensions in characteristic 2, and to totally and weakly
ramified Galois p-extensions in characteristic p. We also apply our results to the non-classical situation where L/K is a finite primitive purely inseparable extension of arbitrary exponent that is acted on, via a higher derivation (but in many different ways), by the divided power K-Hopf algebra. | en_GB |
dc.identifier.citation | Vol. 68 (3), pp. 965-1010. | en_GB |
dc.identifier.doi | 10.5802/aif.3182 | |
dc.identifier.uri | http://hdl.handle.net/10871/28635 | |
dc.language.iso | en | en_GB |
dc.publisher | Association des Annales de l'Institut Fourier | en_GB |
dc.relation.url | http://aif.cedram.org/aif-bin/browse | en_GB |
dc.rights | © Association des Annales de l’institut Fourier, 2018. This article is made available under the terms of the Creative Commons Attribution - No Derivatives 3.0 (France) license: https://creativecommons.org/licenses/by-nd/3.0/fr/ | |
dc.title | Scaffolds and Generalized Integral Galois Module Structure | en_GB |
dc.type | Article | en_GB |
dc.identifier.issn | 0373-0956 | |
dc.description | This is the author accepted manuscript. The final version is available from the Association des Annales de l'Institut Fourier via the DOI in this record. | en_GB |
dc.identifier.journal | Annales de l'Institut Fourier | en_GB |