Skip to main content
SpringerLink
Log in

Ramification Jump in Model Extensions of Degree p

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

An extension of complete dicrete valuation fields with imperfect residue fields is naturally viewed as an epimorphism between algebraic surfaces with a distinguished point. Each regular curve that meets this point with irreducible preimage gives rise to an extension of fields of functions. In this paper, the ramification jump of this extension is considered as a function of a jet of a curve. The Zarisky topology on the set of jets is introduced, and the lower semicontinuity and existence of a common value for the jump are proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Xiao and I. B. Zhukov, “Ramification of higher local fields, approaches, and questions,” preprint (2012).

  2. A. Campillo, Algebroid Curves in Positive Characteristic, Springer-Verlag, New York (1980).

    MATH  Google Scholar 

  3. G.-M. Greuel, C. Lossen, and E. Shustin, Introduction to Singularities and Deformations, Springer-Verlag (2007).

  4. I. B. Zhukov, “Ramification of surfaces: Artin–Schreier extensions,” in: Algebraic Number Theory and Algebraic Geometry, Amer. Math. Soc., Providence, Rhode Island (2002), pp. 211–220.

  5. I. B. Zhukov, “Semiglobal models of extensions of two-dimensional local fields,” Vestn. St.Peterb. Univ., Ser. Mat., Mekh, Astr., 1, 33–38 (2010).

    Article  MathSciNet  Google Scholar 

  6. J.-P. Serre, Local Fields, Springer, New York (1979).

  7. T. T. Moh, “Galois theory of power series rings in characteristic p,” Amer. J. Math., 92, 919–950 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  8. I. B. Zhukov, Commutative Algebra [in Russian], Izd. St.Peterb. Univ., St.Petersburg (2009).

    Google Scholar 

  9. C. T. C. Wall, Singular Points of Plane Curves, Cambridge University Press (2004).

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    I. N. Faizov

Authors
  1. I. N. Faizov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. N. Faizov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 413, 2013, pp. 183–218.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Faizov, I.N. Ramification Jump in Model Extensions of Degree p . J Math Sci 202, 455–478 (2014). https://doi.org/10.1007/s10958-014-2055-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-014-2055-0

Keywords

Search

Navigation