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Quasifinite fields of prescribed characteristic and Diophantine dimension Cover
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|Jul 2024

References

  1. Y. Alemu, On zeros of forms over local fields. Acta Arith. 45 (1985), No. 2, 163-171.
  2. J.Kr. Arason, R. Aravire, R. Baeza, On some invariants of fields of characteristic p > 0. J. Algebra 311 (2007), No. 2, 714-735.
  3. J.K. Arason, R. Baeza, La dimension cohomologique des corps de type Cr en caractéristique p. C. R. Math. Acad. Sci. Paris 348 (2010), No. 3-4, 125-126.
  4. Auel, A., Brussel, E., Garibaldi, S., Vishne, U.: Open problems on central simple algebras. Transform. Groups 16 (2011), 219-264.
  5. G.I. Arkhipov, A.A. Karatsuba, On a problem in the theory of congruences. Russ. Math. Surv. 37 (1982), No. 5, 157-158; translation from Usp. Mat. Nauk 37 (1982), No. 5(227), 161-162 (Russian).
  6. J. Ax, Proof of some conjectures on cohomological dimension. Proc. Amer. Math. Soc. 16 (1965), 1214-1221.
  7. I.D. Chipchakov, On Brauer p-dimensions and absolute Brauer p-dimensions of Henselian fields. J. Pure Appl. Algebra 223 (2019), No. 1, 10-29.
  8. I.D. Chipchakov, Fields of dimension one algebraic over a global or local field need not be of type C1. J. Number Theory 235 (2022), 484-501.
  9. P.M. Cohn, On the decomposition of a field as a tensor product. Glasg. Math. J. 20 (1979), 141-145.
  10. J.-L. Colliot-Thélène, Fields of cohomological dimension one versus C1-fields. Algebra and number theory, 1-6, Hindustan Book Agency, Delhi, 2005.
  11. J.-L. Colliot-Thélène, D.A. Madore, Surfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un. J. Inst. Math. Jussieu 3 (2004), No. 1, 1-16.
  12. P.K. Draxl, Skew Fields. London Math. Soc. Lecture Note Series, 81, Cambridge University Press, Cambridge etc., 1983.
  13. I. Efrat, Valuations, Orderings, and Milnor K-Theory. Math. Surveys and Monographs 124, Amer. Math. Soc., Providence, RI, 2006.
  14. Ph. Gille, T. Szamuely, Central Simple Algebras and Galois Cohomology. Cambridge Studies in Advanced Mathematics, 101. Cambridge Univ. Press, Cambridge, 2006.
  15. M.J. Greenberg, Rational points in Henselian discrete valuation rings. Inst. HautesÉtudes Sci. Publ. Math. No. 31 (1966), 563-568.
  16. O. Izhboldin, p-primary part of the Milnor K-groups and Galois cohomology of fields of characteristic p. In: I. Fesenko, et al. (Eds.), Geom. Topol. Monogr., 3, Invitation to Higher Local Fields, 2000, pp. 19-29.
  17. D. Izquierdo, G.L. Arteche, Homogeneous spaces, algebraic K-theory and cohomological dimensions of fields. J. Eur. Math. Soc. 24 (2022), No. 6, 2169-2189.
  18. K. Kato, Galois cohomology of complete discrete valuation fields. Algebraic K-theory, Proc. Conf., Oberwolfach 1980, Part II, Lect. Notes Math. 967 (1982), 215-238.
  19. K. Kato, T. Kuzumaki, The dimension of fields and algebraic K-theory. J. Number Theory 24 (1986), No. 2, 229-244.
  20. D. Krashen, E. Matzri, Diophantine and cohomological dimensions. Proc. Amer. Math. Soc. 143 (2015), No. 7, 2779-2788.
  21. S. Lang, On quasi algebraic closure. Ann. Math. (2) 55 (1952), 373-390.
  22. S. Lang, Algebra. Revised 3rd ed., Graduate Texts in Math., vol. 211, Springer, New York, 2002.
  23. E. Matzri, Symbol length in the Brauer group of a field, Trans. Amer. Math. Soc. 368 (2016), 413-427.
  24. O.V. Mel’nikov, O.I. Tavgen’, The absolute Galois group of a Henselian field. Dokl. Akad. Nauk BSSR 29 (1985), 581-583.
  25. Merkur’ev, A.S., Simple algebras and quadratic forms. Math. USSR Izv. 38 (1992), No. 1, 215-221; translation from Izv. Akad. Nauk SSSR Ser. Mat. 55 (1991), No. 1, 218-224 (Russian).
  26. M. Nagata, Note on a paper of Lang concerning quasi algebraic closure. Mem. Coll. Sci., Univ. Kyoto, Ser. A, 30 (1957), 237-241.
  27. R. Pierce, Associative Algebras. Graduate Texts in Math., vol. 88, Springer-Verlag, New York-Heidelberg-Berlin, 1982.
  28. J.-P. Serre, Galois Cohomology, Transl. from the French by Patrick Ion, Springer-Verlag, X, Berlin-Heidelberg-New York, 1997.
  29. A.A. Suslin, Algebraic K-theory and the norm residue homomorphism. J. Sov. Math 30 (1985), 2556-2611; translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 25 (1984), 115-207 (Russian).
  30. J.-P. Tignol, A.R. Wadsworth, Value Functions on Simple Algebras, and Associated Graded Rings. Springer Monographs in Math., Springer, Cham-Heidelberg-New York-Dordrecht-London, 2015.
DOI: https://doi.org/10.2478/auom-2024-0017 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 19 - 42
Submitted on: May 25, 2023
Accepted on: Oct 22, 2023
Published on: Jul 10, 2024
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Ivan D. Chipchakov, Boyan B. Paunov, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.