Abstract
Em : A× Ẑ −→ Ẑ (m ∈ N) reflecting the action of A on the meta-abelian quotient π/π′′. In particular, we shall introduce a canonical series of finite index subgroups of A fully exhausting congruity of the invariants Em in a systematical way. Motivation to this paper came from our previous work [N10] where π was given as the fundamental group of an affine elliptic curve E : y = 4x − g2x − g3 over a field K of characteristic zero. A choice of a Krational tangential base point at infinity of the elliptic curve E gives rise to a natural Galois representation φ : Gal(K/K) → A. Given π being presented as ⟨x1,x2, z | [x1,x2]z = 1⟩ so that z generates an inertia over the infinity puncture, we introduced in loc. cit. certain arithmetic invariants Em : Gal(K/K)× Ẑ −→ Ẑ (m ∈ N)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
