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Le Système d’Euler de Kato en Famillie (II)

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Abstract

This article is the second article on the generalization of Kato’s Euler system. The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve, which interpolate the Kato’s Euler systems associated to the modular forms parametrized by the cuspidal eigencurve. We also explain how to use this family of Kato’s Euler system to construct a family of distributions on ℤp over the cuspidal eigencurve; this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.

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Acknowledgements

This work is supported by the Cariparo Eccellenza Grant of the university of Padova, Italy, from 2011 to 2013, by the SFB project 45 of the university of Essen and the SFB project 1085 of the university of Regensburg in German during 2014. The preparation of the this article has been done during my visits of the IMJ and the IHES in France during 2013, and of CRM in Montreal in 2015. I would like to these institutions for their hospitalities.

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  1. School of Mathematics, Renmin University of China, Beijing, 100872, P. R. China

    Shan Wen Wang

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  1. Shan Wen Wang
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Correspondence to Shan Wen Wang.

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Supported by the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grant No. 20XNLG04)

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Wang, S.W. Le Système d’Euler de Kato en Famillie (II). Acta. Math. Sin.-English Ser. 37, 173–204 (2021). https://doi.org/10.1007/s10114-020-8414-5

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