nLab affinoid




In analytic geometry, an affinoid is a sub-space of a unit polydisc, formally dual to an affinoid algebra (see there for more). These are the basic spaces out of which analytic spaces are built by gluing.


We construct non-archimedean SYZ fibrations for maximally degenerate Calabi-Yau varieties, and we show that they are affinoid torus fibrations away from a codimension two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt-models along one-dimensional strata.

Last revised on February 3, 2018 at 09:30:34. See the history of this page for a list of all contributions to it.