Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Open problems in valuation theory in positive characteristic

2017/25/B/ST1/01815

Keywords:

resolution of singularities model theory of valued fields defect deeply ramified fields key polynomials

Descriptors:

  • ST1_2: Algebra
  • ST1_1: Logic and foundations

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Uniwersytet Szczeciński, Wydział Matematyczno-Fizyczny

woj. zachodniopomorskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Franz-Viktor Kuhlmann 

Number of co-investigators in the project: 2

Call: OPUS 13 - announced on 2017-03-15

Amount awarded: 301 620 PLN

Project start date (Y-m-d): 2018-01-19

Project end date (Y-m-d): 2023-01-18

Project duration:: 60 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Laptop (3 000 PLN)

Information in the final report

  • Publication in academic press/journals (18)
  1. Caristi-Kirk and Oettli-Théra ball spaces and applications
    Authors:
    Piotr Blaszkiewicz, Hanna Cmiel, Alessandro Linzi and Piotr Szewczyk
    Academic press:
    Journal of Fixed Point Theory and Applications (rok: 2019, tom: 21, 98, strony: 17), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11784-019-0729-4 - link to the publication
  2. Eliminating tame ramification: generalizations of Abhyankar's Lemma
    Authors:
    Arpan Dutta and Franz-Viktor Kuhlmann
    Academic press:
    Pacific Journal of Mathematics (rok: 2020, tom: 307, strony: 121-136), Wydawca: MSP
    Status:
    Published
    DOI:
    10.2140/pjm.2020.307.121 - link to the publication
  3. Selected methods for the classification of cuts and their applications
    Authors:
    Franz-Viktor Kuhlmann
    Academic press:
    Banach Center Publications (rok: 2020, tom: 121, strony: 85-106), Wydawca: Polish Academy of Sciences Publishing House
    Status:
    Published
    DOI:
    10.4064/bc121-9 - link to the publication
  4. Tame Key polynomials
    Authors:
    Arpan Dutta and Franz-Viktor Kuhlmann
    Academic press:
    Journal of Algebra (rok: 2023, tom: 629, strony: 162-190), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jalgebra.2023.03.032 - link to the publication
  5. Valued fields with finitely many defect extensions of prime degree
    Authors:
    Franz-Viktor Kuhlmann
    Academic press:
    Journal of Algebra and its Applications (rok: 2022, tom: 21, strony: 18), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219498822500499 - link to the publication
  6. Correction and notes to the paper "A classification of Artin-Schreier defect extensions and characterizations of defectless fields"
    Authors:
    Franz-Viktor Kuhlmann
    Academic press:
    Illinois Journal of Mathematics (rok: 2019, tom: 63, strony: 463–468), Wydawca: Duke University Press
    Status:
    Published
    DOI:
    10.1215/00192082-7902469 - link to the publication
  7. Characterizations of Galois extensions with independent defect
    Authors:
    Steven Dale Cutkosky, Franz-Viktor Kuhlmann and Anna Rzepka
    Academic press:
    Selecta mathematica (rok: 2023, tom: ?, strony: 29), Wydawca: Birkhäuser
    Status:
    Submitted
    DOI:
    none - link to the publication
  8. Elimination of Ramification II: Henselian Rationality
    Authors:
    Kuhlmann, F.-V.
    Academic press:
    Israel Journal of Mathematics (rok: 2019, tom: 234, strony: 927–958), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11856-019-1940-0 - link to the publication
  9. On valuation independence and defectless extensions of valued fields
    Authors:
    Pablo Cubides Kovacsics, Franz-Viktor Kuhlmann and Anna Rzepka
    Academic press:
    Journal of Algebra (rok: 2020, tom: 555, strony: 69-95), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jalgebra.2020.02.021 - link to the publication
  10. The valuation theory of deeply ramified fields and its connection with defect extensions
    Authors:
    Franz-Viktor Kuhlmann and Anna Rzepka
    Academic press:
    Transactions of the American Mathematical Society (rok: 2023, tom: 376, strony: 2693–2738), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/tran/8790 - link to the publication
  11. A generic approach to measuring the strength of completeness/compactness of various types of spaces and ordered structures
    Authors:
    Hanna Cmiel, Franz-Viktor Kuhlmann and Katarzyna Kuhlmann
    Academic press:
    Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas (rok: 2021, tom: 115, strony: 44), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s13398-020-00984-3 - link to the publication
  12. On the continuity of roots of polynomials over valued fields
    Authors:
    Hanna Ćmiel, Franz-Viktor Kuhlmann and Piotr Szewczyk
    Academic press:
    Communications in Algebra (rok: 2023, tom: 51, strony: 1383-1412), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/00927872.2022.2137172 - link to the publication
  13. Subfields of algebraically maximal Kaplansky fields
    Authors:
    Franz-Viktor Kuhlmann
    Academic press:
    Communications in Algebra (rok: 2022, tom: ?, strony: 11), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/00927872.2022.2032118 - link to the publication
  14. Approximation types describing extensions of valuations to rational function fields
    Authors:
    Franz-Viktor Kuhlmann
    Academic press:
    Mathematische Zeitschrift (rok: 2022, tom: ?, strony: 38), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-022-02980-2 - link to the publication
  15. Chain intersection closures
    Authors:
    Wieslaw Kubis and Franz-Viktor Kuhlmann
    Academic press:
    Topology and its Applications (rok: 2019, tom: 262, strony: 45615), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.topol.2019.05.009 - link to the publication
  16. Construction of ball spaces and the notion of continuity
    Authors:
    Rene Bartsch, Katarzyna Kuhlmann and Franz-Viktor Kuhlmann
    Academic press:
    New Zealand Journal of Mathematics (rok: 2021, tom: 51, strony: 49-64), Wydawca: New Zealand Mathematical Society & University of Auckland
    Status:
    Published
    DOI:
    brak - link to the publication
  17. Cuts and small extensions of abelian ordered groups
    Authors:
    Franz-Viktor Kuhlmann and Enric Nart
    Academic press:
    Journal of Pure and Applied Algebra (rok: 2022, tom: 226, strony: 29), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jpaa.2022.107103 - link to the publication
  18. Density of Composite places in Function Fields and Application to Real Holomorphy Rings
    Authors:
    Eberhard Becker, Franz-Viktor Kuhlmann and Katarzyna Kuhlmann
    Academic press:
    Mathematisce Nachrichten (rok: 2023, tom: 296, strony: 57-79), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mana.202000308 - link to the publication

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