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Thursday 20 Feb 2020NT Seminar: Mod p>0 reduction of transcendental motives, an arithmetic view

Vladimir Guletskii - University of Liverpool

H103 14:30-16:30

Recently we put forward a guess saying that possibly the transcendental motive of a smooth projective surface over a field of characteristic 0 is integrally indecomposable. In the talk, an outline of a new (yet unpublished) method of proving this expectation will be presented. The main idea behind the method is that integral indecomposability of the transcendental motive can be always lifted from the closed fibre to the generic one, in a smooth projective family of surfaces over the spectrum of a DVR. This allows us to apply the reduction to characteristic p > 0, and then use another result saying that some Fermat hypersurfaces in special positive characteristics have integrally indecomposable transcendental motives over the closure of F_p.

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