Generalized Hirzebruch's conjecture for Hilbert-Picard modular cusps
Shoetsu OGATA
著者情報
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Shoetsu OGATA
MATHEMATICAL INSTITUTE (KAWAUCHI) FACULTY OF SCIENCE TOHOKU UNIVERSITY KAWAUCHI
ジャーナル
フリー
1996 年 22 巻 2 号 p. 385-410
詳細
- Published: 1996 Received: 1994/06/20 Available on J-STAGE: 2008/12/16 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2008/12/16 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : [AMRT] A. Ash, D. Mumford, M. Rapoport and Y. Tai, Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, Brookline, Mass., 1975.
[ABP] M.F. Atiyah, R. Bott and V.K. Patodi, On the heat equation and index theorem, Invent. Math., 19 (1973), 279-330.
[ADS1] M.F. Atiyah, H. Donnelly and LM. Singer, Eta invariants, signature defects of cusps, and values of L-functions, Ann. of Math., 118 (1983), 131-177.
[ADS2] M.F. Atiyah, H. Donnelly and LM. Singer, Signature defects of cusps, and values of L-functions: The nonsplit case, Ann. of Math., 119 (1984), 635-637.
[APS1] M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian ge-ometry I, Math. Proc. Cambridge Philos. Soc., 77 (1975), 43-69.
[APS2] M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian ge-ometry III, Math. Proc. Cambridge Philos. Soc., 79 (1976), 76-99.
[BB] W.L. Bailly, Jr. and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math., 84 (1966), 442-528.
[Gi] P.B. Gilkey, Invariance Theory, The Heat Equation, And the Atiyah-Singer Index Therem, Publish or Perish, Inc., 1984.
[Gr] H. Grauert, Uber Modifikationen and exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
[Hi] F. Hirzebruch, Hilbert modular surfaces, Enseign. Math., 19 (1974), 183-281.
[Ho] R.-P. Holzapfel, Invariants of arithmetic ball quotient surfaces, Math. Nachr., 103 (1981), 117-153.
[I] M.-N. Ishida, The duality of cusp singularities, preprint, (1991).
[MS] H.P. Mckean and LM. Singer, Curvature and eigenvalues of the laplacian, J. Differential Geometry, 1 (1967), 43-69.
[Mo] C.C. Moore, Representations of nilpotent and solvable groups and harmonis analysis on nil and solvmanifolds, Harmonic Analysis on Homogeneous Spaces, (Williamstown, Mass., 1972) Proc. Sympo. Pure Math., 26, Amer. Math. Soc., Providence, RI., 1973, pp. 3-44.
[Mul] W. Muller, Manifolds with Cusps of Rank One, Lecture Notes in Math., 1244, Springer-Verlag, Heidelberg, New York, 1987.
[Mu2] W. Muller, L2-index theory, eta invariants and values of L-functions, Contemp. Math., 105 (1990), 145-189.
[O1] S. Ogata, Signature defects and eta invariants of Picard modular cusp singularities, J. Math. Soc. Japan, 42 (1990), 659-675.
[O2] S. Ogata, Hirzebruch's conjecture on cusp singularities, Math. Ann., 296 (1991), 69-86.
[O3] S. Ogata, Signature defects of Hilbert-Picard modular cusps, Math. Z., 212 (1992), 401-409.
[Sal] I. Satake, On compactifications of the quotient spaces for arithmetically defined discon-tinuous groups, Ann. of Math., 72 (1960), 555-580.
[Sa2] I. Satake, On the y-genus of arithmetic varieties of Q-rank one, Adv. in Math. (Chinese Math. Soc.), 16 (1987), 269-276.
[SO] I. Satake and S. Ogata, Zeta functions associated to cusps and their special values, Automorphic Forms and Geometry of Arithmetic Varieties, (Y. Namikawa and K. Hashimoto eds) Adv. Studies in Pure Math. 15, Kinokuniya, Tokyo and North-Holland, Amsterdam, New York, Oxford, 1989, pp. 1-27.
[Sh] H. Shimizu, On discrete groups acting on the product of upper half planes, Ann. of Math., 77 (1963), 33-71.
[T] H. Tsuchihashi, Higher dimensional analogues of periodic continued fractions and cusp singularities, Tohoku Math. J., 35 (1983), 607-639.
[V] E.B. Vinberg, Theory of homogeneous convex cones, Trans. Moscow Math. Soc., 12 (1967), 303-368.
Right : [AMRT] A. Ash, D. Mumford, M. Rapoport and Y. Tai, Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, Brookline, Mass., 1975.
[ABP] M.F. Atiyah, R. Bott and V.K. Patodi, On the heat equation and index theorem, Invent. Math., 19 (1973), 279-330.
[ADS1] M.F. Atiyah, H. Donnelly and I.M. Singer, Eta invariants, signature defects of cusps, and values of L-functions, Ann. of Math., 118 (1983), 131-177.
[ADS2] M.F. Atiyah, H. Donnelly and I.M. Singer, Signature defects of cusps, and values of L-functions: The nonsplit case, Ann. of Math., 119 (1984), 635-637.
[APS1] M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian geometry I, Math. Proc. Cambridge Philos. Soc., 77 (1975), 43-69.
[APS2] M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian geometry III, Math. Proc. Cambridge Philos. Soc., 79 (1976), 76-99.
[BB] W.L. Bailly, Jr. and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math., 84 (1966), 442-528.
[Gi] P.B. Gilkey, Invariance Theory, The Heat Equation, And the Atiyah-Singer Index Therem, Publish or Perish, Inc., 1984.
[Gr] H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
[Hi] F. Hirzebruch, Hilbert modular surfaces, Enseign. Math., 19 (1974), 183-281.
[Ho] R.-P. Holzapfel, Invariants of arithmetic ball quotient surfaces, Math. Nachr., 103 (1981), 117-153.
[I] M.-N. Ishida, The duality of cusp singularities, preprint, (1991).
[MS] H.P. Mckean and I.M. Singer, Curvature and eigenvalues of the laplacian, J. Differential Geometry, 1 (1967), 43-69.
[Mo] C.C. Moore, Representations of nilpotent and solvable groups and harmonis analysis on nil and solvmanifolds, Harmonic Analysis on Homogeneous Spaces, (Williamstown, Mass., 1972) Proc. Sympo. Pure Math., 26, Amer. Math. Soc., Providence, RI., 1973, pp. 3-44.
[Mul] W. Muller, Manifolds with Cusps of Rank One, Lecture Notes in Math., 1244, Springer-Verlag, Heidelberg, New York, 1987.
[Mu2] W. Muller, L2-index theory, eta invariants and values of L-functions, Contemp. Math., 105 (1990), 145-189.
[O1] S. Ogata, Signature defects and eta invariants of Picard modular cusp singularities, J. Math. Soc. Japan, 42 (1990), 659-675.
[O2] S. Ogata, Hirzebruch's conjecture on cusp singularities, Math. Ann., 296 (1991), 69-86.
[O3] S. Ogata, Signature defects of Hilbert-Picard modular cusps, Math. Z., 212 (1992), 401-409.
[Sal] I. Satake, On compactifications of the quotient spaces for arithmetically defined discon-tinuous groups, Ann. of Math., 72 (1960), 555-580.
[Sa2] I. Satake, On the y-genus of arithmetic varieties of Q-rank one, Adv. in Math. (Chinese Math. Soc.), 16 (1987), 269-276.
[SO] I. Satake and S. Ogata,, Zeta functions associated to cusps and their special values, Automorphic Forms and Geometry of Arithmetic Varieties, (Y. Namikawa and K. Hashimoto eds) Adv. Studies in Pure Math. 15, Kinokuniya, Tokyo and North-Holland, Amsterdam, New York, Oxford, 1989, pp. 1-27.
[Sh] H. Shimizu, On discrete groups acting on the product of upper half planes, Ann. of Math., 77 (1963), 33-71.
[T] H. Tsuchihashi, Higher dimensional analogues of periodic continued fractions and cusp singularities, Tohoku Math. J., 35 (1983), 607-639.
[V] E.B. Vinberg, Theory of homogeneous convex cones, Trans. Moscow Math. Soc., 12 (1967), 303-368.
訂正日: 2008/12/16 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
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