Abstract:
Recent results on the structure of the group K2 of a field and its connections with the Brauer group are presented. The K-groups of Severi–Brauer varieties and simple algebras are computed. A proof is given of Milnor's conjecture that for any field F and natural number n>1 there is the isomorphism Rn,F:K2(F)/nK2(F)∼→nBr(F). Algebrogeometric applications of the main results are presented.
Citation:
A. A. Suslin, “Algebraic K-theory and the norm residue homomorphism”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 25, VINITI, Moscow, 1984, 115–207; J. Soviet Math., 30:6 (1985), 2556–2611
\Bibitem{Sus84}
\by A.~A.~Suslin
\paper Algebraic $K$-theory and the norm residue homomorphism
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1984
\vol 25
\pages 115--207
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd76}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=770942}
\zmath{https://zbmath.org/?q=an:0566.12016|0558.12013}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 30
\issue 6
\pages 2556--2611
\crossref{https://doi.org/10.1007/BF02249123}
Linking options:
https://www.mathnet.ru/eng/intd76
https://www.mathnet.ru/eng/intd/v25/p115
This publication is cited in the following 49 articles:
N. A. Vavilov, “St. Petersburg School of Linear Groups: II. Early Works by Suslin”, Vestnik St.Petersb. Univ.Math., 57:1 (2024), 30
Ivan D. Chipchakov, Boyan B. Paunov, “Quasifinite fields of prescribed characteristic and Diophantine dimension”, Analele Universitatii “Ovidius” Constanta - Seria Matematica, 32:2 (2024), 19
N. A. Vavilov, “Saint Petersburg School of the Theory of Linear Groups. I. Prehistory”, Vestnik St.Petersb. Univ.Math., 56:3 (2023), 273
St. Petersburg Math. J., 34:4 (2023), 715–720
Diego Izquierdo, Giancarlo Lucchini Arteche, “Local-global principles for homogeneous spaces over some two-dimensional geometric global fields”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2021:781 (2021), 165
Wen-Wei Li, “Stable conjugacy and epipelagic L-packets for Brylinski–Deligne covers of Sp(2n)”, Sel. Math. New Ser., 26:1 (2020)
Yong Hu, “Reduced norms of division algebras over complete discrete valuation fields of local-global type”, J. Algebra Appl., 19:11 (2020), 2050217
Philippe Gille, Lecture Notes in Mathematics, 2238, Groupes algébriques semi-simples en dimension cohomologique ≤2, 2019, 55
Abhay Soman, “On triviality of the reduced Whitehead group over Henselian fields”, Arch. Math., 113:3 (2019), 237
Yong Hu, “A Cohomological Hasse Principle Over Two-dimensional Local Rings”, Int Math Res Notices, 2016, rnw149
R. Preeti, A. Soman, “Adjoint groups over Qp(X) and R-equivalence”, Journal of Pure and Applied Algebra, 219:9 (2015), 4254
Manfred Kolster, The Bloch–Kato Conjecture for the Riemann Zeta Function, 2015, 97
Rob de Jeu, James D. Lewis, “Beilinson's Hodge Conjecture for Smooth Varieties”, J K-Theor, 11:2 (2013), 243
R. Preeti, “Classification theorems for hermitian forms, the Rost kernel and Hasse principle over fields withcd2(k)⩽3”, Journal of Algebra, 385 (2013), 294
V. I. Yanchevskiǐ, “Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups”, J. Math. Sci. (N. Y.), 183:5 (2012), 727–747
Philippe Gille, Developments in Mathematics, 18, Quadratic Forms, Linear Algebraic Groups, and Cohomology, 2010, 41
Roozbeh Hazrat, Nikolai Vavilov, “Bak's work on theK-theory of rings”, J K-Theor, 4:1 (2009), 1
Masanori Asakura, Shuji Saito, “Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles”, ANT, 1:2 (2007), 163
Leonid Positselski, “Galois Cohomology of Certain Field Extensions and the Divisible Case of Milnor–Kato Conjecture”, K-Theory, 36:1-2 (2006), 33
Masanori Asakura, “Surjectivity of p-adic regulators on K2 of Tate curves”, Invent. math., 165:2 (2006), 267
Citation in format AMSBIB
Contact us: