Abstract
We give a unified, and somewhat simplified, account of the regulator formulas appearing in papers of Bertolini, Darmon and Rotger, describing the syntomic regulator on the first, second and third self-products of modular curves in terms of p-adic modular forms.
Highlights
1 Introduction In a recent sequence of papers [2,4,11] Bertolini, Darmon and Rotger relate, in several different situations, the syntomic regulator applied to some arithmetic object, to special values of p-adic L-functions
They use the author’s previous work [6,8,9] to find certain formulas for this regulator, which are later related to p-adic L-values
The essential computation is done in the case of diagonal cycles on the triple product of modular curves in [11]
Summary
In a recent sequence of papers [2,4,11] Bertolini, Darmon and Rotger relate, in several different situations, the syntomic regulator applied to some arithmetic object, to special values of p-adic L-functions. They use the author’s previous work [6,8,9] to find certain formulas for this regulator, which are later related to p-adic L-values.
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