Geodesic
Intersections of adelic groups on a~surface
Sbornik. Mathematics, Tome 204 (2013) no. 12, pp. 1701-1711

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We solve a technical problem related to adeles on an algebraic surface. Given a finite set of natural numbers, one can associate with it an adelic group. We show that this operation commutes with taking intersections if the surface is defined over an uncountable field, and we provide a counterexample otherwise. Bibliography: 12 titles.
Keywords: higher adeles, higher-dimensional local rings. 
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     title = {Intersections of adelic groups on a~surface},
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R. Ya. Budylin; S. O. Gorchinskiy. Intersections of adelic groups on a~surface. Sbornik. Mathematics, Tome 204 (2013) no. 12, pp. 1701-1711. http://geodesic.mathdoc.fr/item/SM_2013_204_12_a0/