数理談話会

Rigid geometry has already been developed as one of the possibly conceivable arithmetico-analytic hybrid geometries in last several decades, having nowadays a lot of variants and applications to arithmetic and algebraic problems. Of all such promising variants, the henselian version of the rigid geometry might come as more "genuinely hybrid" between algebraic and analytic geometries, which may expectedly admit several new approaches to, for instance, the arithmetic aspects in the study of algebraic cycles. However, a serious drawback of this new framework, which I will indicate in the talk, is the general failure of GAGA principle in characteristic zero. The main purpose of this talk, then, is to discuss the henselian GAGA principle in positive characteristics. The talk should contain in the first half a brief introduction to the general rigid geometry itself, in order to make it accessible for as many audience as possible.