@article{RM_2007_62_6_a1,
author = {M. Z. Rovinskii},
title = {Automorphism groups of fields, and their representations},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {1121--1186},
year = {2007},
volume = {62},
number = {6},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_2007_62_6_a1/}
}
M. Z. Rovinskii. Automorphism groups of fields, and their representations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 6, pp. 1121-1186. http://geodesic.mathdoc.fr/item/RM_2007_62_6_a1/
[1] N. Jacobson, Lectures in abstract algebra. Vol. III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, NJ–Toronto, ON–London–New York, 1964 | MR | Zbl
[2] I. I. Pjatetskii-Šapiro, I. R. Šafarevič, “Galois theory of transcendental extensions and uniformization”, Amer. Math. Soc. Transl. (2), 69 (1968), 111–145 | MR | Zbl
[3] G. Shimura, “Introduction to the arithmetic theory of automorphic functions”, Kanô Memorial Lectures, No. 1, Publications of the Mathematical Society of Japan, 11, Iwanami Shoten, Publ., Tokyo; Princeton Univ. Press, Princeton, NJ, 1971 ; 14, No 4, 1970, 48–77 ; 14, No 5, 1970, 62–101 | MR | MR | Zbl | Zbl | Zbl
[4] Y. Ihara, On congruence monodromy problems, vol. 1, Lecture Notes, 1, Department of Mathematics, University of Tokyo, 1968 | MR | Zbl | Zbl
[5] W. Krull, “Galoissche Theorie der unendlichen algebraischen Erweiterungen”, Math. Ann., 100:1 (1928), 687–698 | DOI | MR | Zbl
[6] U. Jannsen, “Motives, numerical equivalence, and semi-simplicity”, Invent. Math., 107:3 (1992), 447–452 | DOI | MR | Zbl
[7] M. Rovinsky, “Motives and admissible representations of automorphism groups of fields”, Math. Z., 249:1 (2005), 163–221 ; On certain representations of automorphism groups of an algebraically closed field, , 2001 arXiv: math/0101170 | DOI | MR | Zbl
[8] A. A. Beilinson, “Height pairing between algebraic cycles”, K-theory, arithmetic and geometry (Moscow, 1984–1986), Lecture Notes in Math., 1289, Springer, Berlin, 1987, 1–26 | DOI | MR | Zbl
[9] S. Bloch, Lectures on algebraic cycles, Duke Univ. Math. Ser., IV, Duke University, Mathematics Department, Durham, NC, 1980 | MR | Zbl
[10] A. Beilinson, “Remarks on $n$-motives and correspondences at generic point”, Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), Int. Press Lect. Ser., 3, I, Int. Press, Somerville, MA, 2002, 35–46 | MR | Zbl
[11] M. Rovinsky, Generic cycles, Preprint of the Max-Planck-Institut für Mathematik, MPIM1997-80
[12] M. Rovinsky, “Semilinear representations of PGL”, Selecta Math., 11:3–4 (2005), 491–522 ; , 2003 arXiv: math/0306333 | DOI | MR | Zbl
[13] D. Mumford, “Rational equivalence of 0-cycles on surfaces”, J. Math. Kyoto Univ., 9 (1969), 195–204 | MR | MR | Zbl | Zbl
[14] A. A. Roĭtman, “Rational equivalence of zero-cycles”, Math. USSR-Sb., 18:4 (1972), 571–588 | DOI | MR | Zbl
[15] U. Jannsen, M. Rovinsky, Smooth representations and sheaves, , 2007 arXiv.org: 0707.3914
[16] M. Rovinsky, “Admissible semi-linear representations”, J. Reine Angew. Math., 604 (2007), 159–186 ; , 2005 arXiv.org: math/0506043 | DOI | MR | Zbl
[17] W. Krull, “Endomorphismenringe in der Galoisschen Theorie”, Aequationes Math., 2:2–3 (1969), 269–273 | DOI | MR | Zbl
[18] W. Krull, “Über den Galoisring”, Math. Ann., 185:1 (1970), 25–37 | DOI | MR | Zbl
[19] M. Rovinsky, On maximal proper subgroups of field automorphism groups, , 2006 arXiv.org: math/0601028
[20] D. Lascar, “The group of automorphisms of the field of complex numbers leaving fixed the algebraic numbers is simple”, Model theory of groups and automorphism groups (Blaubeuren, 1995), London Math. Soc. Lecture Note Ser., 244, Cambridge Univ. Press, Cambridge, 1997, 110–114 | MR | Zbl
[21] A. Robert, “Automorphism groups of transcendental field extensions”, J. Algebra, 16:2 (1970), 252–270 | DOI | MR | Zbl
[22] C. J. Ash, J. W. Rosenthal, “Intersections of algebraically closed fields”, Ann. Pure Appl. Logic, 30:2 (1986), 103–119 | DOI | MR | Zbl
[23] O. Ore, “Theory of non-commutative polynomials”, Ann. of Math. (2), 34:3 (1933), 480–508 | DOI | MR | Zbl
[24] W. Krull, “Über eine Verallgemeinerung des Normalkörperbegriffs”, J. Reine Angew. Math., 191 (1953), 54–63 | MR | Zbl
[25] O. Zariski, P. Samuel, Commutative algebra, vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Princeton, NJ–Toronto–London–New York, 1960 | MR | MR | Zbl
[26] M. F. Atiyah, I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley, Reading, MA–London–Don Mills, ON, 1969 | MR | MR | Zbl
[27] F. A. Bogomolov, “Abelian subgroups of Galois groups”, Math. USSR-Izv., 38:1 (1992), 27–67 | DOI | MR | Zbl
[28] F. A. Bogomolov, “On two conjectures in birational algebraic geometry”, Algebraic geometry and analytic geometry (Tokyo, 1990), ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991, 26–52 | MR | Zbl
[29] F. Bogomolov, Yu. Tschinkel, “Commuting elements in Galois groups of function fields”, Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), Int. Press Lect. Ser., 3, I, Int. Press, Somerville, MA, 2002, 75–120 | MR | Zbl
[30] M. Rovinsky, “On certain isomorphisms between absolute Galois groups”, Compositio Math., 136:1 (2003), 61–67 ; , 2000 arXiv.org: math/0011176 | DOI | MR | Zbl
[31] Théorie des topos et cohomologie étale des schémas. Tome 1: Théorie des topos, Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964, Lecture Notes in Math., 269, Springer-Verlag, Berlin–New York, 1972 | DOI | MR | Zbl
[32] P. T. Johnstone, Topos theory, London Mathematical Society Monographs, 10, Academic Press, London–New York–San Francisco, 1977 | MR | MR | Zbl
[33] J. H. Bernstein, A. V. Zelevinskii, “Representations of the group $GL(n,F)$ where $F$ is a non-Archimedean local field”, Russian Math. Surveys, 31:3 (1976), 1–68 | DOI | MR | Zbl
[34] J. S. Milne, Étale cohomology, Princeton Math. Ser., 33, Princeton Univ. Press, Princeton, NJ, 1980 | MR | Zbl
[35] U. Jannsen, “Motivic sheaves and filtrations on Chow groups”, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., 55, Part 1, Amer. Math. Soc., Providence, RI, 1994, 245–302 | MR | Zbl
[36] V. Voevodsky, “Triangulated categories of motives over a field”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 188–238 | MR | Zbl
[37] M. Levine, “Mixed motives”, Math. Surveys Monogr., 57, Amer. Math. Soc., Providence, RI, 1998 | MR | Zbl
[38] M. Hanamura, “Mixed motives and algebraic cycles. I”, Math. Res. Lett., 2:6 (1995), 811–821 ; “Mixed motives and algebraic cycles. III”, Math. Res. Lett., 6:1 (1999), 61–82 | MR | Zbl | MR | Zbl
[39] U. Jannsen, Mixed motives and algebraic $K$-theory, Lecture Notes in Math., 1400, Springer-Verlag, Berlin, 1990 | DOI | MR | Zbl
[40] S. Mac Lane, Categories for the working mathematician, 2nd ed., Grad. Texts in Math., 5, Springer-Verlag, New York, 1998 | MR | Zbl
[41] D. Abramovich, K. Karu, K. Matsuki, J. Włodarczyk, “Torification and factorization of birational maps”, J. Amer. Math. Soc., 15 (2002), 531–572 ; , 1999 arXiv.org: math/9904135 | DOI | MR | Zbl
[42] J. Włodarczyk, Toroidal varieties and the weak factorization theorem, , 1999 arXiv.org: math/9904076 | MR
[43] Ju. I. Manin, “Correspondences, motifs and monoidal transformations”, Math. USSR-Sb., 6:4 (1968), 439–470 | DOI | MR | Zbl
[44] P. Samuel, “Rational equivalence of arbitrary cycles”, Amer. J. Math., 78:2 (1956), 383–400 | DOI | MR | Zbl