>>592 つづき In particular, when one computes the height of a rational point of the projective line minus three points as a suitable weighted sum of the valuations of the q-parameters of the corresponding elliptic curve, one may ignore, up to bounded discrepancies, contributions to the height that arise, say, from the archimedean valuations or from the nonarchimedean valuations that lie over some “exceptional” prime number such as 2.
§ 2.2. Arithmetic degrees as global integrals
§ 2.7. The apparatus and terminology of mono-anabelian transport Example 2.6.1 is exceptionally rich in structural similarities to inter-universal Teichm¨uller theory, which we proceed to explain in detail as follows. One way to understand these structural similarities is by considering the quite substantial portion of terminology of inter-universal Teichm¨uller theory that was, in essence, inspired by Example 2.6.1: (i) Links between “mutually alien” copies of scheme theory: One central aspect of inter-universal Teichm¨uller theory is the study of certain “walls”, or “filters” − which are often referred to as “links” − that separate two “mutually alien” copies of conventional scheme theory [cf. the discussions of [IUTchII], Remark 3.6.2; [IUTchIV], Remark 3.6.1]. The main example of such a link in inter-universal Teichm¨uller theory is constituted by [various versions of] the Θ-link. The log-link also plays an important role in inter-universal Teichm¨uller theory. The main motivating example for these links which play a central role in inter-universal Teichm¨uller theory is the Frobenius morphism ΦηX of Example 2.6.1. From the point of view of the discussion of §1.4, §1.5, §2.2, §2.3, §2.4, and §2.5, such a link corresponds to a change of coordinates.
