The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory
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- by M. J. Hopkins and B. H. Gross PDF
- Bull. Amer. Math. Soc. 30 (1994), 76-86 Request permission
Abstract:
The geometry of the Lubin-Tate space of deformations of a formal group is studied via an étale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex in stable homotopy theory.References
- J. F. Adams, Stable homotopy and generalised homology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0402720
- Ethan S. Devinatz and Michael J. Hopkins, The action of the Morava stabilizer group on the Lubin-Tate moduli space of lifts, Amer. J. Math. 117 (1995), no. 3, 669–710. MR 1333942, DOI 10.2307/2375086
- V. G. Drinfel′d, Elliptic modules, Mat. Sb. (N.S.) 94(136) (1974), 594–627, 656 (Russian). MR 0384707
- Yasushi Fujiwara, On divisibilities of special values of real analytic Eisenstein series, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 35 (1988), no. 2, 393–410. MR 945885
- Phillip A. Griffiths, Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems, Bull. Amer. Math. Soc. 76 (1970), 228–296. MR 258824, DOI 10.1090/S0002-9904-1970-12444-2
- Benedict H. Gross, On canonical and quasicanonical liftings, Invent. Math. 84 (1986), no. 2, 321–326. MR 833193, DOI 10.1007/BF01388810
- M. J. Hopkins and B. H. Gross, Equivariant vector bundles on the Lubin-Tate moduli space, Topology and representation theory (Evanston, IL, 1992) Contemp. Math., vol. 158, Amer. Math. Soc., Providence, RI, 1994, pp. 23–88. MR 1263712, DOI 10.1090/conm/158/01453
- A. Grothendieck, Groupes de Barsotti-Tate et cristaux, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 431–436 (French). MR 0578496
- Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64; With an appendix by P. Deligne. MR 0222093, DOI 10.1007/BFb0080482
- Michael J. Hopkins, Global methods in homotopy theory, Homotopy theory (Durham, 1985) London Math. Soc. Lecture Note Ser., vol. 117, Cambridge Univ. Press, Cambridge, 1987, pp. 73–96. MR 932260 M. J. Hopkins and D. C. Ravenel, The chromatic tower (in preparation).
- Michael J. Hopkins and Jeffrey H. Smith, Nilpotence and stable homotopy theory. II, Ann. of Math. (2) 148 (1998), no. 1, 1–49. MR 1652975, DOI 10.2307/120991
- Luc Illusie, Déformations de groupes de Barsotti-Tate (d’après A. Grothendieck), Astérisque 127 (1985), 151–198 (French). Seminar on arithmetic bundles: the Mordell conjecture (Paris, 1983/84). MR 801922
- Nicholas Katz, Travaux de Dwork, Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 409, Lecture Notes in Math., Vol. 317, Springer, Berlin, 1973, pp. 167–200 (French, with English summary). MR 0498577
- Nicholas M. Katz, $p$-adic $L$-functions, Serre-Tate local moduli, and ratios of solutions of differential equations, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 365–371. MR 562628
- Nicholas M. Katz, Crystalline cohomology, Dieudonné modules, and Jacobi sums, Automorphic forms, representation theory and arithmetic (Bombay, 1979), Tata Inst. Fund. Res. Studies in Math., vol. 10, Tata Institute of Fundamental Research, Bombay, 1981, pp. 165–246. MR 633662
- Nicholas M. Katz, Divisibilities, congruences, and Cartier duality, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 667–678 (1982). MR 656042
- Jonathan Lubin and John Tate, Formal moduli for one-parameter formal Lie groups, Bull. Soc. Math. France 94 (1966), 49–59. MR 238854, DOI 10.24033/bsmf.1633
- B. Mazur and William Messing, Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Mathematics, Vol. 370, Springer-Verlag, Berlin-New York, 1974. MR 0374150, DOI 10.1007/BFb0061628
- Haynes R. Miller, Douglas C. Ravenel, and W. Stephen Wilson, Periodic phenomena in the Adams-Novikov spectral sequence, Ann. of Math. (2) 106 (1977), no. 3, 469–516. MR 458423, DOI 10.2307/1971064
- Jack Morava, Noetherian localisations of categories of cobordism comodules, Ann. of Math. (2) 121 (1985), no. 1, 1–39. MR 782555, DOI 10.2307/1971192
- Daniel Quillen, On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969), 1293–1298. MR 253350, DOI 10.1090/S0002-9904-1969-12401-8
- Douglas C. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984), no. 2, 351–414. MR 737778, DOI 10.2307/2374308
- Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics, vol. 121, Academic Press, Inc., Orlando, FL, 1986. MR 860042
- Jiu-Kang Yu, On the moduli of quasi-canonical liftings, Compositio Math. 96 (1995), no. 3, 293–321. MR 1327148
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 30 (1994), 76-86
- MSC (2000): Primary 55N22; Secondary 11S31, 14F30, 14L05, 55P42
- DOI: https://doi.org/10.1090/S0273-0979-1994-00438-0
- MathSciNet review: 1217353