Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions

S. V. Vostokov, N. V. Haustov, I. B. Zhukov, O. Yu Ivanova, S. S. Afanas’eva

Research output

Abstract

Ramification in complete discrete valuation fields is studied. For the case of a perfect residue field, there is a well-developed theory of ramification groups. Hyodo introduced the concept of ramification depth associated with the different of an extension and obtained an inequality that combines the concept of ramification depth in a degree p2 cyclotomic extension with the concept of ramification depth in a degree p subextension. The paper gives a detailed consideration of the structure of degree p2 extensions that can be obtained by a composite of two degree p extensions. In this case, it is not required that the residue field be perfect. Using the concepts of wild and ferocious extensions and the defect of the main unit, degree p2 extensions are classified and more accurate estimates for the ramification depth are obtained. In a number of cases, exact formulas for ramification depth are presented.

Original languageEnglish
Pages (from-to)114-123
Number of pages10
JournalVestnik St. Petersburg University: Mathematics
Volume51
Issue number2
DOIs
Publication statusPublished - 1 Apr 2018

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Ramification
Analogue
Cyclotomic
Valuation
Defects
Composite
Unit
Concepts
Estimate

Scopus subject areas

  • Mathematics(all)

Cite this

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abstract = "Ramification in complete discrete valuation fields is studied. For the case of a perfect residue field, there is a well-developed theory of ramification groups. Hyodo introduced the concept of ramification depth associated with the different of an extension and obtained an inequality that combines the concept of ramification depth in a degree p2 cyclotomic extension with the concept of ramification depth in a degree p subextension. The paper gives a detailed consideration of the structure of degree p2 extensions that can be obtained by a composite of two degree p extensions. In this case, it is not required that the residue field be perfect. Using the concepts of wild and ferocious extensions and the defect of the main unit, degree p2 extensions are classified and more accurate estimates for the ramification depth are obtained. In a number of cases, exact formulas for ramification depth are presented.",
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Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions. / Vostokov, S. V.; Haustov, N. V.; Zhukov, I. B.; Ivanova, O. Yu; Afanas’eva, S. S.

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 2, 01.04.2018, p. 114-123.

Research output

TY - JOUR

T1 - Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions

AU - Vostokov, S. V.

AU - Haustov, N. V.

AU - Zhukov, I. B.

AU - Ivanova, O. Yu

AU - Afanas’eva, S. S.

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