I will discuss two notions of tameness for smooth, proper varieties defined over a field equipped with a discrete valuation, which are only interesting if the residual characteristic is positive: cohomological tameness, and logarithmic good reduction. The first notion is weaker than the second one, by a fundamental result of C. Nakayama. They are equivalent for curves (by work of T. Saito and J. Stix), and I will say some words about the reasons. I will prove that they are also equivalent for abelian varieties (joint work of the speaker and A. Bellardini); this can be seen as a logarithmic version of the Néron-Ogg-Shafarevich criterion. If time permits, I will also discuss some further questions and partial results on the geometry of log smooth degenerations.
Freitag, den 11. November 2016 um 13:30 Uhr, in INF 205, SR C Freitag, den 11. November 2016 at 13:30, in INF 205, SR C
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Dr. Giulia Battiston