Title: Hida families, p-adic heights, and derivatives
Abstract: This paper concerns the arithmetic of certain p-adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a p-adic regulator, and the derivative of a p-adic L-function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first conjecture implies the equivalence of the last two.