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志村 五郎 (1971)
Introduction to the arithmetic theory of automorphic functions
M. Bertolini, H. Darmon (1996)
Heegner points on Mumford–Tate curvesInventiones mathematicae, 126
J. Boutot, H. Carayol (1991)
Uniformisation p-adique des courbes de Shimura : les théorèmes de Čerednik et de DrinfeldAstérisque
B. Gordon, James Lewis, S. Müller–Stach, S. Saito, N. Yui (2000)
The Arithmetic and Geometry of Algebraic Cycles
S. Lang (1971)
Algebraic Number Theory
B. Gross, D. Zagier (1986)
Heegner points and derivatives ofL-seriesInventiones mathematicae, 84
J. Nekovář (1992)
Kolyvagin's method for Chow groups of Kuga-Sato varietiesInventiones mathematicae, 107
S. Dasgupta, J. Teitelbaum (2007)
The p-adic upper half plane
M. Tretkoff, G. Shimura (1971)
Introduction to the Arithmetic Theory of Automorphic FunctionsMathematics of Computation, 26
J. Nekovář (1995)
On thep-adic height of Heegner cyclesMathematische Annalen, 302
R. Coleman (1985)
Torsion points on curves and p-adic Abelian integralsAnnals of Mathematics, 121
E-mail address: masdeu@math.columbia
R. Greenberg, G. Stevens (1993)
p-adicL-functions andp-adic periods of modular formsInventiones mathematicae, 111
R. Coleman, B. Gross (1989)
$p$-adic Heights on Curves
Shou-wu Zhang (1997)
Heights of Heegner cycles and derivatives of L-seriesInventiones mathematicae, 130
J. Murre, C. Deninger (1991)
Motivic decomposition of abelian schemes and the Fourier transform.Journal für die reine und angewandte Mathematik (Crelles Journal), 1991
M. Baker, B. Conrad, S. Dasgupta, K. Kedlaya, J. Teitelbaum (2008)
-adic Geometry: Lectures from the 2007 Arizona Winter School, 45
(1982)
Dilogarithms, regulators and p-adic L-functions
A. Iovita, Michael Spiess (2001)
Derivatives of p-adic L-functions, Heegner cycles and monodromy modules attached to modular formsInventiones mathematicae, 154
J. Fresnel, M. Put (2003)
Rigid analytic geometry and its applications
B. Birch, H. Swinnerton-Dyer (1963)
Notes on elliptic curves. I.Journal für die reine und angewandte Mathematik (Crelles Journal), 1963
J. Nekovář (2002)
On p-adic height pairings
M. Bertolini, H. Darmon (1998)
Heegner points, p-adic L-functions, and the Cerednik-Drinfeld uniformizationInventiones mathematicae, 131
B. Perrin-Riou (1992)
Théorie d'Iwasawa et hauteursp-adiquesInventiones mathematicae, 109
(2003)
Hidden structures on semi-stable curves
A. Wiles (1995)
Modular Elliptic Curves and Fermat′s Last Theorem(抜粋) (フェルマ-予想がついに解けた!?), 34
H. Darmon (2003)
Rational Points on Modular Elliptic Curves
(1995)
CM cycles over Shimura curves
(1988)
Le corps des periodes p-adiques
E. Shalit (1989)
Eichler cohomology and periods of modular forms on p-adic Schottky groups.Journal für die reine und angewandte Mathematik (Crelles Journal), 1989
N. Katz, Tadao Oda (1968)
On the differentiation of De Rham cohomology classes with respect to parametersJournal of Mathematics of Kyoto University, 8
S. David (1993)
Séminaire de Théorie des Nombres, Paris, 1990–91
M. Bertolini, H. Darmon (1999)
$p$-adic periods, $p$-adic $L$-functions, and the $p$-adic uniformization of Shimura curvesDuke Mathematical Journal, 98
(2011)
Masdeu, CM cycles on Shimura curves, and p-adic L-functions, Preprint (2011), arXiv:1110.6465v1 [math.NT
J. Fontaine, B. Perrin-Riou (1994)
Autour des conjectures de Bloch et Kato: cohomologie galoisienne et valeurs de fonctions L
J. Coates (2005)
Coleman Integration Versus Schneider Integration on Semistable Curves To
(1987)
A formula for the cup product on Mumford curves
IllueYl fioYle (2005)
Values ofp-adic L-functions and a p-adic Poisson kernel
B. Moonen (2011)
On the Chow motive of an abelian scheme with non-trivial endomorphismsCrelle's Journal, 2016
G. Faltings (1988)
p-adic Hodge theoryJournal of the American Mathematical Society, 1
P. Schneider (1984)
Rigid-analytic L - transforms
M. Bertolini, H. Darmon, Kartik Prasanna (2013)
Generalized heegner cycles and p-adic rankin L-seriesDuke Mathematical Journal, 162
P. Colmez, J. Fontaine (2000)
Construction des représentations p-adiques semi-stablesInventiones mathematicae, 140
B. Mazur, J. Tate, J. Teitelbaum (1986)
Onp-adic analogues of the conjectures of Birch and Swinnerton-DyerInventiones mathematicae, 84
B. Mazur, P. Swinnerton-Dyer (1974)
Arithmetic of Weil curvesInventiones mathematicae, 25
J. Nekovář (2000)
-adic Abel-Jacobi maps and -adic heights
M. Bertolini, H. Darmon, A. Iovita, Michael Spiess (2002)
Teitelbaum's exceptional zero conjecture in the anticyclotomic settingAmerican Journal of Mathematics, 124
Siegfried Bosch, Ulrich Güntzer, R. Remmert (1984)
Non-Archimedean Analysis
L-Functions and Tamagawa Numbers of Motives
R. Coleman (1989)
Reciprocity laws on curvesCompositio Mathematica, 72
H. Jager (1984)
Number Theory Noordwijkerhout 1983
V. Guillemin
Hodge Theory
P. Cartier, L. Illusie, N. Katz, G. Laumon, Y. Manin, K. Ribet (2007)
The Grothendieck Festschrift : A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck
AbstractLet f be a modular form of weight k≥2 and level N, let K be a quadratic imaginary field and assume that there is a prime p exactly dividing N. Under certain arithmetic conditions on the level N and the field K, one can attach to this data a p-adic L-function Lp (f,K,s) , as done by Bertolini–Darmon–Iovita–Spieß in [Teitelbaum’s exceptional zero conjecture in the anticyclotomic setting, Amer. J. Math. 124 (2002), 411–449]. In the case of p being inert in K, this analytic function of a p-adic variable s vanishes in the critical range s=1,…,k−1 , and one may be interested in the values of its derivative in this range. We construct, for k≥4 , a Chow motive endowed with a distinguished collection of algebraic cycles which encode these values, via the p-adic Abel–Jacobi map. Our main result generalizes the result obtained by Iovita and Spieß in [Derivatives of p-adic L-functions, Heegner cycles and monodromy modules attached to modular forms, Invent. Math. 154 (2003), 333–384], which gives a similar formula for the central value s=k/2 . Even in this case our construction is different from the one found by Iovita and Spieß.
Compositio Mathematica – Cambridge University Press
Published: May 15, 2012
Keywords: 11G40 (primary); 11F11; 11G18 (secondary); CM cycles; Shimura curve; p -adic integration; anti-cyclotomic p -adic L -function
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