an:06099199
Zbl 1303.11060
Seveso, Marco Adamo
\(p\)-adic \(L\)-functions and the rationality of Darmon cycles
EN
Can. J. Math. 64, No. 5, 1122-1181 (2012).
00307673
2012
j
11F67 14G05
\(p\)-adic \(L\)-functions; modular symbols; \({\mathcal L}\)-invariants; \(p\)-adic integration theory; Darmon cycles; \(p\)-adic Gross-Zagier type formulas
The proof of the first result (Theorem 1.1) follows the strategy developed by \textit{M. Bertolini} and \textit{H. Darmon} [Invent. Math. 168, No. 2, 371--431 (2007; Zbl 1129.11025); Ann. Math. (2) 170, No. 1, 343--369 (2009; Zbl 1203.11045)] in this weight two setting. Also, \(p\)-adic Gross-Zagier type formulas formulated in Theorems 1.2 and 1.3 are higher weight analogs of the corresponding results given by Bertolini and Darmon [loc. cit.]. One of the main technical new ingredients are both the ``modular symbol theoretic'' \(p\)-adic integration theory and the ``cohomological theoretic'' \(p\)-adic integraion theory developed in a recent paper by \textit{V. Rotger} and \textit{M. A. Seveso} [J. Eur. Math. Soc. (JEMS) 14, No. 6, 1955--1999 (2012; Zbl 1292.11069)].
Andrzej D??browski (Szczecin)
Zbl 1129.11025; Zbl 1203.11045; Zbl 1292.11069