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Infinite Towers of Galois Defect Extensions of Kaplansky Fields Cover

Infinite Towers of Galois Defect Extensions of Kaplansky Fields

By: Anna Blaszczok  
Open Access
|Aug 2018

References

  1. [1] Blaszczok A., Infinite towers of Artin-Schreier defect extensions of rational function fields, in: A. Campillo, F.-V. Kuhlmann, B. Teissier (Eds.), Valuation theory in interaction, EMS Series of Congress Reports, European Mathematical Society (EMS), Zürich, 2014, pp. 16-54.10.4171/149-1/3
  2. [2] Blaszczok A., Distances of elements in valued field extensions, submitted.
  3. [3] Blaszczok, A., Kuhlmann F.-V., Algebraic independence of elements in immediate extensions of valued fields, J. Algebra 425 (2015), 179-214.10.1016/j.jalgebra.2014.10.050
  4. [4] Blaszczok A., Kuhlmann F.-V., On maximal immediate extensions of valued fields, Math. Nachr. 290 (2017), 7-18.10.1002/mana.201500073
  5. [5] Endler O., Valuation theory, Springer-Verlag, Berlin, 1972.10.1007/978-3-642-65505-0
  6. [6] Kaplansky I., Maximal fields with valuations, Duke Math. J. 9 (1942), 303-321.
  7. [7] Karpilovsky G., Topics in field theory, North-Holland Mathematics Studies 155, North-Holland Publishing Co., Amsterdam, 1989.
  8. [8] Krull W., Allgemeine Bewertungstheorie, J. Reine Angew. Math. 167 (1932), 160-196.
  9. [9] Kuhlmann F.-V., Henselian function fields and tame fields, preprint (extended version of Ph.D. thesis), Heidelberg, 1990.
  10. [10] Kuhlmann F.-V., Valuation theoretic and model theoretic aspects of local uniformization, in: H. Hauser, J. Lipman, F. Oort, A. Quirós (Eds.), Resolution of singularities. A research textbook in tribute to Oscar Zariski, Progress in Mathematics 181, Birkhäuser Verlag, Basel, 2000, pp. 381-456.10.1007/978-3-0348-8399-3_15
  11. [11] Kuhlmann F.-V., Value groups, residue fields, and bad places of rational function fields, Trans. Amer. Math. Soc. 356 (2004), 4559-4600.10.1090/S0002-9947-04-03463-4
  12. [12] Kuhlmann F.-V., A classification of Artin-Schreier defect extensions and characterizations of defectless fields, Illinois J. Math. 54 (2010), 397-448.
  13. [13] Kuhlmann F.-V., The defect, in: M. Fontana, S.-E. Kabbaj, B. Olberding, I. Swanson (Eds.), Commutative algebra. Noetherian and non-Noetherian perspectives, Springer- Verlag, New York, 2011, pp. 277-318.10.1007/978-1-4419-6990-3_11
  14. [14] Kuhlmann F.-V., The algebra and model theory of tame valued fields, J. Reine Angew. Math. 719 (2016), 1-43.
  15. [15] Kuhlmann F.-V., Elimination of ramification II: henselian rationality of valued function fields, in preparation.
  16. [16] Whaples G., Galois cohomology of additive polynomial and n-th power mappings of fields, Duke Math. J. 24 (1957), 143-150.
DOI: https://doi.org/10.1515/amsil-2017-0012 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 65 - 78
Submitted on: Apr 1, 2017
Accepted on: Nov 8, 2017
Published on: Aug 24, 2018
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2018 Anna Blaszczok, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.