Algorithm for determining the type of a singular fiber in an elliptic pencil. (English) Zbl 1214.14020

Birch, B.J. (ed.) et al., Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 - August 3, 1972. Lect. Notes Math. 476, 33-52 (1975).
See the review of the entire collection in Zbl 0315.14014.
This is a slightly edited version of a letter to Cassels.
Tate’s absence from the conference was in protest against the large scale support of basic scientific research by military organizations rather than by agencies whose aims and spirit he thinks are more compatible with those of scientific inquiry.
Contents: 0. Summary. 1. Generalised Weierstrass form. 2. Change of coordinates. 3. “Minimal Weierstrass equation” over a valuation ring. 4. The canonical filtration on the group of \(v\)-adic points. 5. Application: The relation between \(L_v(1)\) and \(\int_{E_v}|\infty_v|\) in case \(k\) is finite. 6. The Néron minimum model. 7. Algorithm analysing singular fibers (first five cases). 8. Algorithm continued (last five cases).
For the entire collection see [Zbl 0315.14014].


14G25 Global ground fields in algebraic geometry
14K15 Arithmetic ground fields for abelian varieties


Zbl 0315.14014
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