메뉴 건너뛰기




Volumn 140, Issue 4, 2004, Pages 887-951

Derivatives of Eisenstein series and Faltings heights

Author keywords

Arithmetic geometry; Eisenstein series; Heights; Shimura curves

Indexed keywords


EID: 4644261897     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0010437X03000459     Document Type: Article
Times cited : (66)

References (49)
  • 3
    • 84968513706 scopus 로고
    • Heights of projective varieties and positive Green forms
    • J.-B. Bost, H. Gillet and C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994), 903-1027.
    • (1994) J. Amer. Math. Soc , vol.7 , pp. 903-1027
    • Bost, J.-B.1    Gillet, H.2    Soulé, C.3
  • 4
  • 6
    • 0033096455 scopus 로고    scopus 로고
    • Potential theory and Lefschetz theorems for arithmetic surfaces
    • J.-B. Bost, Potential theory and Lefschetz theorems for arithmetic surfaces, Ann. Sci. École Norm. Sup. 32 (1999), 241-312.
    • (1999) Ann. Sci. École Norm. Sup , vol.32 , pp. 241-312
    • Bost, J.-B.1
  • 7
    • 43449097273 scopus 로고    scopus 로고
    • C. L. Chai and G. Faltings, Degeneration of abelian varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, 22 (Springer, Berlin, 1990).
    • C. L. Chai and G. Faltings, Degeneration of abelian varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, vol. 22 (Springer, Berlin, 1990).
  • 8
    • 0000860654 scopus 로고
    • Sums involving the values at negative integers of L-functions of quadratic characters
    • H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217 (1975), 271-285.
    • (1975) Math. Ann , vol.217 , pp. 271-285
    • Cohen, H.1
  • 9
    • 0001272794 scopus 로고
    • Périodes des variétés abéliennes à multiplication complexe
    • P. Colmez, Périodes des variétés abéliennes à multiplication complexe, Ann. of Math. (2) 138 (1993), 625-683.
    • (1993) Ann. of Math. (2) , vol.138 , pp. 625-683
    • Colmez, P.1
  • 10
    • 51649181666 scopus 로고
    • Irreducibility of the space of curves of a given genus
    • P. Deligne and D. Mumford, Irreducibility of the space of curves of a given genus, Publ. Math. IHES 36 (1969), 75-109.
    • (1969) Publ. Math. IHES , vol.36 , pp. 75-109
    • Deligne, P.1    Mumford, D.2
  • 11
    • 0000133160 scopus 로고
    • Les schémas de modules des courbes elliptiques
    • Modular functions of one variable II, Antwerp, Springer, Berlin
    • P. Deligne and M. Rapoport, Les schémas de modules des courbes elliptiques, in Modular functions of one variable II, Antwerp. 1972. Lecture Notes in Mathematics, vol. 349 (Springer, Berlin, 1973), 143-316.
    • (1972) Lecture Notes in Mathematics , vol.349 , pp. 143-316
    • Deligne, P.1    Rapoport, M.2
  • 12
    • 0002084363 scopus 로고
    • Coverings of p-adic symmetric regions
    • V. G. Drinfeld, Coverings of p-adic symmetric regions, Funct. Anal. Appl. 10 (1977), 29-40.
    • (1977) Funct. Anal. Appl , vol.10 , pp. 29-40
    • Drinfeld, V.G.1
  • 14
    • 34250151276 scopus 로고
    • Endlichkeilssätze für abelsche Varietäten über Zahlkörpern
    • G. Faltings, Endlichkeilssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366.
    • (1983) Invent. Math , vol.73 , pp. 349-366
    • Faltings, G.1
  • 16
    • 0036036964 scopus 로고    scopus 로고
    • Heegner divisors and, non-holomorphic modular forms
    • J. Funke, Heegner divisors and, non-holomorphic modular forms, Compositio Math. 133 (2002), 289-321.
    • (2002) Compositio Math , vol.133 , pp. 289-321
    • Funke, J.1
  • 17
    • 0009219392 scopus 로고
    • Weil's representation and the spectrum of the metaplectic group
    • Springer, New York
    • S. Gelbart, Weil's representation and the spectrum of the metaplectic group, Lecture Notes in Mathematics, vol. 530 (Springer, New York, 1976).
    • (1976) Lecture Notes in Mathematics , vol.530
    • Gelbart, S.1
  • 18
    • 0002622581 scopus 로고
    • On canonical and quasi-canonical liftings
    • B. H. Gross, On canonical and quasi-canonical liftings, Invent. Math. 84 (1986), 321-326.
    • (1986) Invent. Math , vol.84 , pp. 321-326
    • Gross, B.H.1
  • 19
    • 51249171685 scopus 로고
    • Arithmetic intersection theory
    • H. Gillet and C. Soulé, Arithmetic intersection theory, Publ. Math. IHES 72 (1990), 93-174.
    • (1990) Publ. Math. IHES , vol.72 , pp. 93-174
    • Gillet, H.1    Soulé, C.2
  • 20
    • 0011289288 scopus 로고    scopus 로고
    • Moduli of Riemann surfaces, transcendental aspects
    • Abdus Salam Int. Cent. Theoret. Phys, Trieste
    • R. Hain, Moduli of Riemann surfaces, transcendental aspects, ICTP Lecture Notes, vol. 1 (Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2000), 293-353.
    • (2000) ICTP Lecture Notes , vol.1 , pp. 293-353
    • Hain, R.1
  • 21
    • 0002131804 scopus 로고
    • Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
    • F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Invent. Math. 38 (1976), 57-113.
    • (1976) Invent. Math , vol.38 , pp. 57-113
    • Hirzebruch, F.1    Zagier, D.2
  • 22
    • 84968502589 scopus 로고
    • Points on some, Shimura varieties over finite fields
    • R. Kottwitz. Points on some, Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (1992), 373-444.
    • (1992) J. Amer. Math. Soc , vol.5 , pp. 373-444
    • Kottwitz, R.1
  • 23
    • 0033239398 scopus 로고    scopus 로고
    • Arithmetic Hirzebruch-Zagier cycles
    • S. Kudla and M. Rapoport, Arithmetic Hirzebruch-Zagier cycles, J. reine angew. Math. 515 (1999), 155-244.
    • (1999) J. reine angew. Math , vol.515 , pp. 155-244
    • Kudla, S.1    Rapoport, M.2
  • 24
    • 0034348173 scopus 로고    scopus 로고
    • Height pairings on Shimura curves and p-adic unformization
    • S. Kudla and M. Rapoport, Height pairings on Shimura curves and p-adic unformization, Invent. Math. 142 (2000), 153-223.
    • (2000) Invent. Math , vol.142 , pp. 153-223
    • Kudla, S.1    Rapoport, M.2
  • 25
    • 0042185039 scopus 로고    scopus 로고
    • Cycles on Siegel threefolds and derivatives of Eisenstein series
    • S. Kudla and M. Rapoport, Cycles on Siegel threefolds and derivatives of Eisenstein series, Ann. Sci. École Norm. Sup. 33 (2000), 695-756.
    • (2000) Ann. Sci. École Norm. Sup , vol.33 , pp. 695-756
    • Kudla, S.1    Rapoport, M.2
  • 27
    • 0346390509 scopus 로고    scopus 로고
    • On the, derivative of an Eisenstein series of weight 1
    • S. Kudla, M. Rapoport and T. Yang, On the, derivative of an Eisenstein series of weight 1, Int. Math. Res. Notices 7 (1999), 347-385.
    • (1999) Int. Math. Res. Notices , vol.7 , pp. 347-385
    • Kudla, S.1    Rapoport, M.2    Yang, T.3
  • 28
    • 51249170573 scopus 로고
    • Splitting metaplectic covers of dual reductive pairs
    • S. Kudla, Splitting metaplectic covers of dual reductive pairs, Israel J. Math. 87 (1992), 361-401.
    • (1992) Israel J. Math , vol.87 , pp. 361-401
    • Kudla, S.1
  • 29
    • 0009193851 scopus 로고    scopus 로고
    • Algebraic cycles on Shimura varieties of orthogonal type
    • S. Kudla, Algebraic cycles on Shimura varieties of orthogonal type, Duke Math. J. 86 (1997), 39-78.
    • (1997) Duke Math. J , vol.86 , pp. 39-78
    • Kudla, S.1
  • 30
    • 0031320233 scopus 로고    scopus 로고
    • Central derivatives of Eisenstein series and, height pairings
    • S. Kudla, Central derivatives of Eisenstein series and, height pairings, Ann. of Math. (2) 146 (1997), 545-646.
    • (1997) Ann. of Math. (2) , vol.146 , pp. 545-646
    • Kudla, S.1
  • 33
    • 43449093210 scopus 로고    scopus 로고
    • S. Kudla, Eisenstein series and arithmetic geometry, in Proc. ICM, II (Higher Ed. Press, Beijing, 2002), 173-183.
    • S. Kudla, Eisenstein series and arithmetic geometry, in Proc. ICM, vol. II (Higher Ed. Press, Beijing, 2002), 173-183.
  • 34
    • 0038801425 scopus 로고    scopus 로고
    • Integrals of Borcherds forms
    • S. Kudla, Integrals of Borcherds forms, Compositio Math. 137 (2003), 293-349.
    • (2003) Compositio Math , vol.137 , pp. 293-349
    • Kudla, S.1
  • 35
    • 33745322963 scopus 로고    scopus 로고
    • Modular forms and arithmetic geometry
    • International Press, Boston
    • S. Kudla, Modular forms and arithmetic geometry, in Current Developments in Mathematics (International Press, Boston, 2003), 135-180.
    • (2003) Current Developments in Mathematics , pp. 135-180
    • Kudla, S.1
  • 36
    • 0037804867 scopus 로고    scopus 로고
    • Generalized arithmetic intersection numbers
    • U. Kühn, Generalized arithmetic intersection numbers, J. reine angew. Math. 534 (2001), 209-236.
    • (2001) J. reine angew. Math , vol.534 , pp. 209-236
    • Kühn, U.1
  • 39
    • 0007033878 scopus 로고
    • A generalization of the Chowla-Selberg formula
    • Y. Nakkajima and Y. Taguchi, A generalization of the Chowla-Selberg formula, J. reine angew. Math. 419 (1991), 119-124.
    • (1991) J. reine angew. Math , vol.419 , pp. 119-124
    • Nakkajima, Y.1    Taguchi, Y.2
  • 40
    • 84967594482 scopus 로고
    • On some explicit formulas in the theory of Weil representations
    • R. Rao, On some explicit formulas in the theory of Weil representations, Pacific J. Math. 157 (1993), 335-371.
    • (1993) Pacific J. Math , vol.157 , pp. 335-371
    • Rao, R.1
  • 43
    • 0040294957 scopus 로고
    • Confluent hypergeometric functions on tube domains
    • G. Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), 269-302.
    • (1982) Math. Ann , vol.260 , pp. 269-302
    • Shimura, G.1
  • 44
    • 0000364967 scopus 로고
    • Intersection theory on algebraic stacks and on their moduli spaces
    • A. Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Invent. Math. 97 (1989), 613-670.
    • (1989) Invent. Math , vol.97 , pp. 613-670
    • Vistoli, A.1
  • 46
    • 34250594733 scopus 로고
    • Sur certains groupes d'opérateurs unitaires
    • A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1984), 143-211.
    • (1984) Acta Math , vol.111 , pp. 143-211
    • Weil, A.1
  • 48
    • 0001070973 scopus 로고    scopus 로고
    • An explicit formula for local densities of quadratic forms
    • T. H. Yang, An explicit formula for local densities of quadratic forms, J. Number Theory 72 (1998), 309-356.
    • (1998) J. Number Theory , vol.72 , pp. 309-356
    • Yang, T.H.1
  • 49
    • 0040995820 scopus 로고
    • Nombres de classes et formes modulaires de poids 3/2
    • D. Zagier, Nombres de classes et formes modulaires de poids 3/2, C. R. Acad. Sci. Paris 281 (1975), 883-886.
    • (1975) C. R. Acad. Sci. Paris , vol.281 , pp. 883-886
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.