Heegner Points on X ... (11)
This paper concerns the arithmetic of certain -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 -adic regulator, and the derivative of a -adic -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first...
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case, many things simplify and we are thus able to prove a more precise structure theorem than in the general case.
We establish “higher depth” analogues of regularized determinants due to Milnor for zeros of cuspidal automorphic -functions of over a general number field. This is a generalization of the result of Deninger about the regularized determinant for zeros of the Riemann zeta function.
Let be a -adic local field with residue field such that and be a -adic representation of . Then, by using the theory of -adic differential modules, we show that is a Hodge-Tate (resp. de Rham) representation of if and only if is a Hodge-Tate (resp. de Rham) representation of where is a certain -adic local field with residue field the smallest perfect field containing .