16 Jan
1993
16 Jan
'93
3:47 a.m.
Well, there is a lot of problems in the arithmetic of cubical surfaces. There is a book by Yu.I.Manin called "Cubical surfaces" which was written in sixties and as far as I know most of the conjectures are still open (see also recent reviews by Manin & Co.. on the arithmetic of rational varities). It is very nice and hard part of the arithmetic algebraic geometry which is in a way a generalization of the classical arithmetic of elliptic curves. I really doubt that toposes (especially ringed toposes...) can be of much help here mostly because the theory of toposes is much more elementary thing than all these arithmetical problems. Vladimir Voevodsky. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++