p-adic heights and Vologodsky integration

We extend the result of a previous work to the case of curves with semi-stable reduction. In this case, one can replace Coleman integration by Vologodsky integration to extend the Coleman-Gross definition of a $p$-adic height pairing. we show that this pairing still equals the one defined by Nekovar.

[1]  B. Chiarellotto,et al.  Algebraic versis Rigid Cohomology with Logarithmic Coefficients , 1994 .

[2]  R. Coleman.  Reciprocity laws on curves , 1989 .

[3]  Sarah Livia Zerbes,et al.  Vologodsky integration on curves with semi-stable reduction , 2017, Israel Journal of Mathematics.

[4]  Kazuya Kato,et al.  L-Functions and Tamagawa Numbers of Motives , 2007 .

[5]  Nicolas Bourbaki,et al.  Groupes et algèbres de Lie , 1971 .

[6]  Einzelwerken Muster,et al.  Invent , 2021, Encyclopedic Dictionary of Archaeology.

[7]  AMNON BESSER,et al.  On the syntomic regulator for K1 of a surface , 2012 .

[8]  Amnon Besser,et al.  Syntomic regulators andp-adic integration I: Rigid syntomic regulators , 2000 .

[9]  권경학,et al.  4 , 1906, Undiscovered Country.

[10]  The p-adic height pairings of Coleman-Gross and of Nekovar , 2002, math/0209006.

[11]  Robert F. Coleman,et al.  Torsion points on curves and p-adic Abelian integrals , 1985 .

[12]  A. Gabriel.  Editor , 2018, Best "New" African Poets 2018 Anthology.

[13]  Robert F. Coleman,et al.  Dilogarithms, regulators andp-adicL-functions , 1982 .

[14]  B. M. Fulk.  MATH , 1992 .

[15]  Amnon Besser,et al.  The syntomic regulator for $K_4$ of curves , 2012, 1208.0516.

[16]  P. Colmez.  Intégration sur les variétés p-adiques , 1998 .

[17]  p-adic Arakelov theory , 2003, math/0301029.

[18]  Amnon Besser.  Coleman integration using the Tannakian formalism , 2000, math/0011269.

[19]  J. Nekovář.  On p-adic height pairings , 2002 .

[20]  Amnon Besser,et al.  Syntomic regulators andp-adic integration II:K2 of curves , 2000 .