A Carlitz module analogue of the Grunwald-Wang Theorem

Nguyen, Dong Quan Ngoc

doi:10.1512/iumj.2018.67.7319

Cited by 1 publication

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The answer is affirmative in many cases, but there are counterexamples too (see in particular [52,Theorem 18]). In [70], Dong Quan Ngoc Nguyen studied a generalization of such a problem for Carlitz modules over function fields and generalizes van der Heiden's results by giving some sufficient conditions to have an affirmative answer.…”

Section: E Tors (K)| B(d)mentioning

confidence: 90%

“…In particular they showed some counterexamples to Problem 1.2 in elliptic curves and also some counterexamples to Cassels' question. An analogue of Problem 1.2 for Drinfeld modules and respectively Carlitz modules was studied in [52,70]. In [52], van der Heiden considered the problem for Drinfeld modules of rank 1 and rank 2 over function fields.…”

Section: E Tors (K)| B(d)mentioning

confidence: 99%

See 1 more Smart Citation

Local-global questions for divisibility in commutative algebraic groups

Dvornicich

Paladino

2022

European Journal of Mathematics

View full text Add to dashboard Cite

This is a survey focusing on the Hasse principle for divisibility of points in commutative algebraic groups and its relation with the Hasse principle for divisibility of elements of the Tate–Shavarevich group in the Weil–Châtelet group. The two local-global subjects arose as a generalization of some classical questions considered respectively by Hasse and Cassels. We describe the deep connection between the two problems and give an overview of the long-established results and the ones achieved during the last twenty years, when the questions were taken up again in a more general setting. In particular, by connecting various results about the two problems, we describe how some recent developments in the first of the two local-global questions imply an answer to Cassels’ question, which improves all the results published before about that problem. This answer is best possible over $${\mathbb Q}$$ Q . We also describe some links with other similar questions, for example the Support Problem and the local-global principle for existence of isogenies of prime degree in elliptic curves.

show abstract

Section: E Tors (K)| B(d)mentioning

confidence: 90%