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Geldhauser, Nikita; Lavrenov, Andrei; Petrov, Victor; Sechin, Pavel. Morava J-invariant. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e104. doi: 10.1017/fms.2025.10041
@article{10_1017_fms_2025_10041,
author = {Geldhauser, Nikita and Lavrenov, Andrei and Petrov, Victor and Sechin, Pavel},
title = {Morava {J-invariant}},
journal = {Forum of Mathematics, Sigma},
pages = {e104},
year = {2025},
volume = {13},
number = {1},
doi = {10.1017/fms.2025.10041},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2025.10041/}
}
TY - JOUR AU - Geldhauser, Nikita AU - Lavrenov, Andrei AU - Petrov, Victor AU - Sechin, Pavel TI - Morava J-invariant JO - Forum of Mathematics, Sigma PY - 2025 SP - e104 VL - 13 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2025.10041/ DO - 10.1017/fms.2025.10041 ID - 10_1017_fms_2025_10041 ER -
[1] , Stable Homotopy and Generalised Cohomology (Chicago Lectures in Mathematics Series) (University of Chicago Press, Chicago, 1974). Google Scholar
[2] , ‘Hopf structures attached to K-theory: Hodgkin’s theorem’, Ann. of Math. 85(2), (1967), 508–525.10.2307/1970356 Google Scholar | DOI
[3] , Lie Groups (Graduate Texts in Mathematics) vol. 225 (Springer-Verlag New York, 2004).10.1007/978-1-4757-4094-3 Google Scholar | DOI
[4] , and , ‘Invariants, torsion indices and oriented cohomology of complete flags’, Ann. Sci. Ec. Norm. Super. (4) 46(3) (2013), 405–448.10.24033/asens.2192 Google Scholar | DOI
[5] and , ‘On the Balmer spectrum of the Morel–Voevodsky category’, Duke Math. J. 174(6) (2025), 1013–1044.10.1215/00127094-2024-0051 Google Scholar | DOI
[6] , and , The Algebraic and Geometric Theory of Quadratic Forms (Colloquium Publications) vol. 56 (Providence, RI, 2008).10.1090/coll/056 Google Scholar | DOI
[7] , and , ‘Shells of twisted flag varieties and the Rost invariant’, Duke Math. J. 165(2) (2016), 285–339.10.1215/00127094-3165434 Google Scholar | DOI
[8] and , ‘Degree invariant of ’, Int. Math. Res. Not. 19 (2010), 3746–3762. Google Scholar
[9] , , and , ‘Morava K-theory of orthogonal groups and motives of projective quadrics’, Adv. Math. 446 (2024), 109657.10.1016/j.aim.2024.109657 Google Scholar | DOI
[10] , ‘Torsion homologique et sections rationnelles’, Sem. C. Chevalley (ENS 1958, exposé 5, Secreatariat Math.) (IHP, Paris, 1958). Google Scholar
[11] , ‘On the K-theory of Lie groups’, Topology 6 (1967), 1–36.10.1016/0040-9383(67)90010-9 Google Scholar | DOI
[12] and , ‘Schubert calculus for algebraic cobordism’, J. Reine Angew. Math. 656 (2011), 59–85. Google Scholar
[13] , , and , ‘Higher torsion in Lie groups’, J. Math. Soc. Japan 50(4) (1998), 801–818.10.2969/jmsj/05040801 Google Scholar | DOI
[14] , and , ‘Hopf algebra structure of mod 2 Cohomology of Simple Lie Groups’, Publ. RIMS, Kyoto Univ. 12 (1976), 141–167.10.2977/prims/1195190961 Google Scholar | DOI
[15] and , ‘BP operations and Morava’s extraordinary K-theories’, Math. Z. 144 (1975), 55–75.10.1007/BF01214408 Google Scholar | DOI
[16] , ‘Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups’, Invent. Math. 80 (1985), 69–79.10.1007/BF01388548 Google Scholar | DOI
[17] , , and , The Book of Involutions (Colloquium Publications) vol. 44 (AMS, 1998).10.1090/coll/044 Google Scholar | DOI
[18] , ‘The algebraic K-theory of the classical groups and some twisted forms’, Duke Math. J. 70(2) (1993), 405–443.10.1215/S0012-7094-93-07008-1 Google Scholar | DOI
[19] and , Algebraic Cobordism (Springer Monographs in Mathematics) (Springer-Verlag Berlin Heidelberg, 2007). Google Scholar
[20] and , ‘Quotients of MGL, their slices and their geometric parts’, Doc. Math., Extra volume: Alexander S. Merkurjev’s Sixtieth Birthday (2015), 407–442. Google Scholar
[21] , ‘Anneaux de Chow des groupes algébriques , , et ’, in Publications Mathématiques d’Orsay, vol. 95 (Université de Paris XI, U.E.R. Mathématique, Orsay, 1974), 74–119. Google Scholar
[22] , ‘Comparison of the equivariant and the ordinary K-theory of algebraic varieties’, St Petersburg Math. J. 9(4) (1998), 815–850. Google Scholar
[23] and , ‘On the structure of Hopf Algebras’, Ann. of Math. 81(2) (1965), 211–264.10.2307/1970615 Google Scholar | DOI
[24] and , ‘Hopf algebra structure of Morava K-theory of the exceptional Lie Groups’, Contemp. Math. 293 (2002), 195–231.10.1090/conm/293/04949 Google Scholar | DOI
[25] , ‘Eine nichtgeometrische Konstruktion der Spektren und Multiplikative Automorphismen von ’, Diplomarbeit (Johann Wolfgang Goethe-Universität Frankfurt, 1995). Google Scholar
[26] , ‘On the structure of for ’, Trans. A mer. Math. Soc. 354(5) (2002), 1749–1757.10.1090/S0002-9947-02-02920-3 Google Scholar | DOI
[27] , ‘Higher torsion in the Morava K-theory of and ’, J. Math. Soc. Japan 53(2) (2001), 383–394.10.2969/jmsj/05320383 Google Scholar | DOI
[28] and , ‘Morava K-theory of twisted flag varieties,’ Preprint, 2014, . Google Scholar | arXiv
[29] and , ‘Hopf-theoretic approach to motives of twisted flag varieties’, Comp. Math. 157(5) (2021), 963–996.10.1112/S0010437X2100703X Google Scholar | DOI
[30] , and , ‘-invariant of linear algebraic groups’, Ann. Sci. École Norm. Sup. 41 (2008), 1023–1053.10.24033/asens.2088 Google Scholar | DOI
[31] , ‘The integral homology and cohomology rings for and ’, J. Pure Appl. Algebra 73 (1991), 105–153.10.1016/0022-4049(91)90108-E Google Scholar | DOI
[32] , ‘The bar spectral sequence converging to ’, Manuscripta Math. 65(1) (1989), 47–61.10.1007/BF01168366 Google Scholar | DOI
[33] , ‘On the Morava K-theories of ’, Proc. of AMS 108(4) (1990), 1031–1038. Google Scholar
[34] , ‘ is not homotopy nilpotent for ’, Topology 32(2) (1993), 239–249.10.1016/0040-9383(93)90017-P Google Scholar | DOI
[35] , ‘Towards the algebra structure of the Morava K-theory of the orthogonal groups’, Manuscripta Math. 94(3) (1997), 287–301.10.1007/BF02677854 Google Scholar | DOI
[36] , ‘Remarks on the Morava K-theories of special orthogonal groups’, Int. J. Pure Appl. Math. 43(3) (2008), 423–434. Google Scholar
[37] , ‘Remarks on , Int. J. Pure Appl. Math. 79(3) (2012), 473–480. Google Scholar
[38] , ‘Complex cobordism and stable homotopy groups of spheres’, Bull. Amer. Math. Soc. (N.S.) 18(1) (1988), 88–91. Google Scholar
[39] , On Thom Spectra, Orientability, and Cobordism (Springer Monogr. Math.) (Springer-Verlag, Berlin, 1998). Google Scholar
[40] , ‘Motivic construction of cohomological invariants’, Comment. Math. Helv. 91(1) (2016), 163–202.10.4171/cmh/382 Google Scholar | DOI
[41] and , ‘Applications of the Morava K-theory to algebraic groups’, Ann. Sci. Éc. Norm. Sup. 54(4) (2021), 945–990. Google Scholar
[42] , ‘Products on -modules’, Trans. Amer. Math. Soc. 351(7) (1999), 2569–2606.10.1090/S0002-9947-99-02436-8 Google Scholar | DOI
[43] , ‘On the Chow groups of quadratic Grassmannians’, Doc. Math. 10 (2005), 111–130.10.4171/dm/184 Google Scholar | DOI
[44] , ‘Fields of -invariant , in Algebra, Arithmetic and Geometry , Manin Festschrift (Progress in Mathematics) vol. 270 (Birkhäuser, 2007), 661–686. Google Scholar
[45] , ‘Isotropic motives’, Inst. Math. Jussieu 21(4) (2022), 1271–1330.10.1017/S1474748020000560 Google Scholar | DOI
[46] , ‘Isotropic and numerical equivalence for Chow groups and Morava K-theories’, Invent. Math. 237 (2024), 779–808.10.1007/s00222-024-01267-z Google Scholar | DOI
[47] , ‘Bloch–Kato conjecture for -coefficients and algebraic Morava -theories’, Preprint, 1995, http://web.archive.org/web/20220120011232/https://faculty.math.illinois.edu/K-theory/0076/morbk.pdf Google Scholar
[48] , ‘On products in a family of cohomology theories associated to the invariant prime ideals of ’, Comment. Math. Helv. 52 (1977), 457–481.10.1007/BF02567379 Google Scholar | DOI
[49] , ‘Commutative ring-spectra of characteristic 2’, Comment. Math. Helv. 61 (1986), 33–45.10.1007/BF02621900 Google Scholar | DOI
[50] , ‘Brown-Peterson cohomology groups of exceptional Lie groups’, J. Pure Appl. Algebra 17 (1980), 223–226.10.1016/0022-4049(80)90086-9 Google Scholar | DOI
[51] , ‘On mod odd prime Brown-Peterson cohomology groups of exceptional Lie groups’, J. Math. Soc. Japan 34:2 (1982), 293–305.10.2969/jmsj/03420293 Google Scholar | DOI
[52] , ‘Algebraic cobordism of simply connected Lie groups’, Math. Proc. Cambridge Philos. Soc. 139(2) (2005), 243–260.10.1017/S0305004105008510 Google Scholar | DOI
[53] , ‘Applications of Atiyah–Hirzebruch spectral sequences for Motivic cobordism’, Proc. London Math. Soc. 90(3), (2005), 783–816.10.1112/S0024611504015084 Google Scholar | DOI
[54] , ‘Definitions and examples of algebraic Morava K-theories,’ Preprint, 2025, . Google Scholar | arXiv
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