The boundary of the eisenstein symbol

Abstract

A sign confusion crept into the calculations leading to Proposition 3.2 of the above article: the normalisation of Po,-.-,P, used in Sect. 1 to define the Eisenstein symbol does not lead to the usual Steinberg symbol in the case of K2. Thus the first displayed formula following 3.1 (p. 311) should read This has the effect of replacing the term d 'j(v-~t) Further results are not affected.

Surjectivity of p-adic regulators on K 2 of Tate curves

“…Let E/R be the Néron model of E L /L, and G m,k ⊂ E k the identity component of the special fiber. Let [21] for more calculation of the boundary). This implies…”

“…It is based on the fact that dimH 2 ét (E K , Q l (2)) = 1 for l = p whereas dimH 2 ét (E K , Q p (2)) = 2[K : Q p ] + 1 where [K : Q p ] denotes the degree of K over Q p . In the l-adic case we only need to construct one K 2 -symbol which has nontrivial boundary (see [21] for more calculation of the boundary). However it is not enough in the p-adic case.…”

Mahler measures, K-theory and values of L-functions

“…Using this notation we have the following formula which is due to Schappacher and Scholl (see [16] chapter 3):…”

“…in MM K and force it to be a short exact sequence (16) 0 → H 1 (E K )(1) → H 1 (U K )(1) → ker(j * ) → 0.…”

Beĭlinson’s conjectures

“…If X /Q is an elliptic curve without complex multiplication but with a nontrivial torsion over Q, one can repeat the construction of 7.4 and get an element of H 2 M (X, Q(2)), but not necessarily of H 2 (X, Q(2)) Z . Amusingly, the obstruction to integrality is related to the third Bernoulli polynomial in [11], [60]. In fact, it was only after the calculations of [11] that the cohomology of the integral model was incorporated into the conjectures.…”