naa a22 4500 510783252 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0072-6 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0072-6 Algebraic equations on the adèlic closure of a Drinfeld module [Elektronische Daten] [Dragos Ghioca, Thomas Scanlon] Let k be a field of positive characteristic and K = k(V) a function field of a variety V over k and let A K be the ring of adèles of K with respect to the places on K corresponding to the divisors on V. Given a Drinfeld module $$\Phi :\mathbb{F}[t] \to End_K (\mathbb{G}_a )$$ over K and a positive integer g we regard both K g and A K g as $$\Phi \left( {\mathbb{F}_p [t]} \right)$$ -modules under the diagonal action induced by Φ. For Γ ⊆ K g a finitely generated $$\Phi \left( {\mathbb{F}_p [t]} \right)$$ -submodule and an affine subvariety $$X \subseteq \mathbb{G}_a^g$$ defined over K, we study the intersection of X(A K ), the adèlic points of X, with $$\bar \Gamma$$ , the closure of Γ with respect to the adèlic topology, showing under various hypotheses that this intersection is no more than X(K) ∩ Γ. Hebrew University Magnes Press, 2012 Ghioca Dragos Department of Mathematics, University of British Columbia, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada aut Scanlon Thomas Department of Mathematics, Evans Hall, University of California, 94720-3840, Berkeley, CA, USA aut Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 461-483 0021-2172 194:1<461 2013 194 11856 https://doi.org/10.1007/s11856-012-0072-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0072-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ghioca Dragos Department of Mathematics, University of British Columbia, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada aut NATIONALLICENCE 700 1- Scanlon Thomas Department of Mathematics, Evans Hall, University of California, 94720-3840, Berkeley, CA, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 461-483 0021-2172 194:1<461 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer