A Note on Critical p-adic L-functions

Abstract

We study the adjunction property of the Jacquet-Emerton functor in certain neighborhoods of critical points in the eigencurve. As an application, we construct two-variable p-adic L-functions around critical points via Emerton’s representation theoretic approach.

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Acknowledgements

I want to thank Matthew Emerton for suggesting the problem of extending his adjunction formula to critical points on the eigencurve, that led to the note. I thank Daniel Barrera Salazar, John Bergdall, Xin Wan, Shanwen Wang for helpful discussions or remarks. I also thank the anonymous referee for the reading and helpful suggestions.

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Correspondence to Yi Wen Ding.

Additional information

Supported by EPSRC (Grant No. EP/L025485/1) and (Grant No. 7101500268) from Peking University

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Ding, Y.W. A Note on Critical p-adic L-functions. Acta. Math. Sin.-English Ser. 37, 121–141 (2021). https://doi.org/10.1007/s10114-020-8396-3

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Keywords

  • p-adic L-function
  • eigencurve
  • critical p-stabilization
  • Jacquet-Emerton functor

MR(2010) Subject Classification

  • 11F67
  • 11S80