Document Type
Article
Publication Date
10-6-2026
Department
Mathematics
Abstract
In this working paper, we report our recent efforts concerning a possible characteristic p analog of the so-called converse of Abel's theorem discussed by Darboux and Griffiths. The characteristic zero version is used in one proof of the Lie-Wirtinger theorem on double translation manifolds and also in related aspects of the geometry of webs. In informal terms, our results indicate that, apart from some isolated counterexamples, formal power series Abel relations over an algebraically closed field of characteristic p essentially only arise in the (generalized) Jacobians of algebraic curves. The ultimate goal is to complete thevwork started in the author's PhD thesis from 1980. Some of the results we will discuss have thus far only been established via symbolic computation over fields of small characteristic and hence the general statement remains conjectural.
Repository Citation
Little, John B., "Progress towards an analog of the Darboux-Griffiths converse of Abel's theorem in characteristic p" (2026). Mathematics and Computer Science Department Faculty Scholarship. 29.
https://crossworks.holycross.edu/math_fac_scholarship/29