References
- Y. Alemu, On zeros of forms over local fields. Acta Arith. 45 (1985), No. 2, 163-171.
- J.Kr. Arason, R. Aravire, R. Baeza, On some invariants of fields of characteristic p > 0. J. Algebra 311 (2007), No. 2, 714-735.
- 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.
- Auel, A., Brussel, E., Garibaldi, S., Vishne, U.: Open problems on central simple algebras. Transform. Groups 16 (2011), 219-264.
- 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).
- J. Ax, Proof of some conjectures on cohomological dimension. Proc. Amer. Math. Soc. 16 (1965), 1214-1221.
- 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.
- 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.
- P.M. Cohn, On the decomposition of a field as a tensor product. Glasg. Math. J. 20 (1979), 141-145.
- J.-L. Colliot-Thélène, Fields of cohomological dimension one versus C1-fields. Algebra and number theory, 1-6, Hindustan Book Agency, Delhi, 2005.
- 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.
- P.K. Draxl, Skew Fields. London Math. Soc. Lecture Note Series, 81, Cambridge University Press, Cambridge etc., 1983.
- I. Efrat, Valuations, Orderings, and Milnor K-Theory. Math. Surveys and Monographs 124, Amer. Math. Soc., Providence, RI, 2006.
- Ph. Gille, T. Szamuely, Central Simple Algebras and Galois Cohomology. Cambridge Studies in Advanced Mathematics, 101. Cambridge Univ. Press, Cambridge, 2006.
- M.J. Greenberg, Rational points in Henselian discrete valuation rings. Inst. HautesÉtudes Sci. Publ. Math. No. 31 (1966), 563-568.
- 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.
- 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.
- 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.
- K. Kato, T. Kuzumaki, The dimension of fields and algebraic K-theory. J. Number Theory 24 (1986), No. 2, 229-244.
- D. Krashen, E. Matzri, Diophantine and cohomological dimensions. Proc. Amer. Math. Soc. 143 (2015), No. 7, 2779-2788.
- S. Lang, On quasi algebraic closure. Ann. Math. (2) 55 (1952), 373-390.
- S. Lang, Algebra. Revised 3rd ed., Graduate Texts in Math., vol. 211, Springer, New York, 2002.
- E. Matzri, Symbol length in the Brauer group of a field, Trans. Amer. Math. Soc. 368 (2016), 413-427.
- O.V. Mel’nikov, O.I. Tavgen’, The absolute Galois group of a Henselian field. Dokl. Akad. Nauk BSSR 29 (1985), 581-583.
- 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).
- M. Nagata, Note on a paper of Lang concerning quasi algebraic closure. Mem. Coll. Sci., Univ. Kyoto, Ser. A, 30 (1957), 237-241.
- R. Pierce, Associative Algebras. Graduate Texts in Math., vol. 88, Springer-Verlag, New York-Heidelberg-Berlin, 1982.
- J.-P. Serre, Galois Cohomology, Transl. from the French by Patrick Ion, Springer-Verlag, X, Berlin-Heidelberg-New York, 1997.
- 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).
- 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.