The abelian monodromy extension property for families of curves
β Scribed by Sabin Cautis
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 448 KB
- Volume
- 344
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let E=K be an elliptic curve defined over a number field, let Δ₯ be the canonical height on E; and let K ab =K be the maximal abelian extension of K: Extending work of M. Baker (IMRN 29 (2003) 1571-1582), we prove that there is a constant CΓ°E=KΓ40 so that every nontorsion point PAEΓ°K ab Γ satisfies Δ₯
2 Γ 2 . If H is abelian of order 8, we may use K = k H \* , and if H is abelian of order 4 we use K = kD 8 \* . If H βΌ = D 8 , then in the two possible examples, one has K = kD 8 \* and the other has K = kQ 8 \* . If H βΌ = 2 Γ 2 Γ 2 then H has two simple degree 2 characters, Ο 1 and Ο 2 , and they