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The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory

Authors: M. J. Hopkins and B. H. Gross
Journal: Bull. Amer. Math. Soc. 30 (1994), 76-86
MSC (2000): Primary 55N22; Secondary 11S31, 14F30, 14L05, 55P42
MathSciNet review: 1217353
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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.

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  • [1] J. F. Adams, Stable homotopy and generalised homology, Univ. of Chicago Press, Chicago, 1974. MR 0402720 (53:6534)
  • [2] E. Devinatz and M. J. Hopkins, The action of the Morava stabilizer group on the Lubin-Tate moduli space of lifts, submitted to Amer. J. Math. MR 1333942 (97a:55007)
  • [3] V. G. Drinfel'd, Elliptic modules, Math. USSR-Sb. 23 (1974), 561-592. MR 0384707 (52:5580)
  • [4] Y. Fujiwara, On divisibilities of special values of real analytic Eisenstein series, J. Fac. Sci. Univ. Tokyo 35 (1988), 393-410. MR 945885 (90e:11070)
  • [5] P. 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 0258824 (41:3470)
  • [6] B. H. Gross, On canonical and quasi-canonical liftings, Invent. Math. 84 (1986), 321-326. MR 833193 (87g:14051)
  • [7] B. H. Gross and M. J. Hopkins, Equivariant vector bundles on the Lubin-Tate moduli space (to appear in Proceedings of the Northwestern conference on algebraic topology and representation theory, Contemp. Math. (Eric Friedlander and Mark Mahowald, eds.), Amer. Math. Soc, Providence, RI). MR 1263712 (95b:14033)
  • [8] A. Grothendieck, Groupes de Barsotti-Tate et cristaux, Actes Congress Internat. Math., Nice (Paris), vol. 1, Gauthier-Villar, Paris, 1971, pp. 431-436. MR 0578496 (58:28211)
  • [9] R. Hartshorne, Residues and duality, Lecture Notes in Math., vol. 20, Springer-Verlag, New York, 1966. MR 0222093 (36:5145)
  • [10] M. J. Hopkins, Global methods in homotopy theory, Proceedings of the 1985 London Math. Soc. Symposium on Homotopy Theory (J. D. S. Jones and E. Rees, eds.), Cambridge Univ. Press, Cambridge, 1987, pp. 73-96. MR 932260 (89g:55022)
  • [11] M. J. Hopkins and D. C. Ravenel, The chromatic tower (in preparation).
  • [12] M. J. Hopkins and J. H. Smith, Nilpotence and stable homotopy theory. II (to appear in Ann. of Math.). MR 1652975 (99h:55009)
  • [13] L. Illusie, Déformations de groupes de Barsotti-Tate, Seminaire sur les pinceaux arithmétiques: la conjecture de Mordell, Asterisque 127 (1985), 151-198. MR 801922
  • [14] N. Katz, Travaux de Dwork, Sem. Bourbaki, 1971/1972 (Berlin and New York), Lecture Notes in Math., vol. 417, Springer-Verlag, New York, 1973, exposé 409, pp. 431-436. MR 0498577 (58:16672)
  • [15] -, p-Adic L-functions, Serre-Tate local moduli, and ratios of solutions of differential equations, Proceedings of the ICM, Helsinki, 1978, pp. 365-371. MR 562628 (81d:12012)
  • [16] -, Crystelline cohomology, Dieudonné modules and Jacobi sums, Automorphic Forms, Representation Theory and Arithmetic, Tata Institute of Fundamental Research, Bombay, 1979, pp. 165-246. MR 633662 (83a:14022)
  • [17] -, Divisibilities, congruences, and Cartier duality, J. Fac. Sci. Univ. Tokyo 28 (1981), 667-678. MR 656042 (83h:10067)
  • [18] J. Lubin and J. Tate, Formal moduli for one parameter formal Lie groups, Bull. Soc. Math. France 94 (1966), 49-60. MR 0238854 (39:214)
  • [19] B. Mazur and W. Messing, Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Math., vol. 370, Springer-Verlag, Berlin and New York, 1974. MR 0374150 (51:10350)
  • [20] H. R. Miller, D. C. Ravenel, and W. S. Wilson, Periodic phenomena in the Adams-Novikov spectral sequence, Ann. of Math. (2) 106 (1977), 469-516. MR 0458423 (56:16626)
  • [21] J. Morava, Noetherian localizations of categories of cobordism comodules, Ann. of Math. (2) 121 (1985), 1-39. MR 782555 (86g:55004)
  • [22] D. G. Quillen, On the formal group laws of oriented and unoriented cobordism theory, Bull. Amer. Math. Soc. 75 (1969), 1293-1298. MR 0253350 (40:6565)
  • [23] D. C. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984), 351-414. MR 737778 (85k:55009)
  • [24] -, Complex cobordism and stable homotopy groups of spheres, Academic Press, New York, 1986. MR 860042 (87j:55003)
  • [25] J.-K. Yu, On the moduli of quasi-canonical liftings, submitted to Compositio Math. MR 1327148 (97b:11144)

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Keywords: Chromatic tower, formal groups, Lubin-Tate space, Morava K-theory
Article copyright: © Copyright 1994 American Mathematical Society

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