Multiplicative relations of points on algebraic groups

• Autorzy: Flicker Y. Z. , Krasoń P.

Identyfikatory

DOI

10.4064/ba8104-8-2017

• Języki publikacji: EN

Abstrakty

EN

Our aim here is to restructure the area of multiplicative relations on points and congruences, by proposing a novel conjecture in the context of general reductive linear algebraic groups. To support our conjecture we check it in a few elementary but new cases, and claim this extends classical work in number theory on multiplicative relations on points and congruences, initiated by Skolem and Schinzel, which we rephrase group-theoretically as Hasse principles on commutative linear algebraic groups, or tori, so that a part of it becomes the abelian case of our conjecture. Our conjecture can then be viewed as an extension to general-not necessarily commutative-reductive linear algebraic groups of a part of Schinzel's result. We relate it to the Erdős support problem. To motivate our conjecture from another perspective we note that analogues have been extensively developed for abelian varieties. We give a short account of this, and state a question on the ʺdetecting linear dependence" problem.

Słowa kluczowe

EN

linear algebraic groups; rational points; multiplicative relations; Hasse principle

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2017
• Tom: Vol. 65, no. 2
• Strony: 125--138
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Flicker Y. Z.

• Ariel University, Ariel 40700, Israel
• The Ohio State University, Columbus, OH 43210, U.S.A.

autor

Krasoń P.

• University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).