The paper is devoted to ramification theory for a class of complete discrete valuation fields, which includes 2-dimensional local fields of prime characteristic p. It is proved that any finite extension of such a field can be modified into an extension with zero ramification depth by means of an infinite elementary Abelian base change.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. B. Zhukov, “Ramification in elementary Abelian extensions,” Zap. Nauchn. Semin. POMI, 413, 106–114 (2013).
L. Xiao and I. Zhukov, “Ramification in the imperfect residue field case, approaches and questions,” St.Petersb. Math. J., 26, No. 5 (2015).
E. F. Lysenko, “Ramification in a cyclic extension of degree p 2 of a complete discrete valuation field of prime characteristic p with imperfect residue field,” Zap. Nauchn. Semin. POMI, 413, 153–172 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 423, 2014, pp. 126–131.
Rights and permissions
About this article
Cite this article
Zhukov, I.B. The Elementary Abelian Conductor. J Math Sci 209, 564–567 (2015). https://doi.org/10.1007/s10958-015-2513-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-015-2513-3