Konstantinos Kartas: Nonstandard methods in almost mathematics

Almost mathematics – introduced by Faltings and developed by Gabber–Ramero – is a technical toolkit in commutative algebra and plays a central role in modern p-adic geometry. We present a nonstandard approach based on ultraproducts – originating with Gabber and independently rediscovered by Jahnke and the speaker – that turns “almost” properties into genuine ones. We also present a nonstandard version of the almost purity theorem. Joint work in progress with Franziska Jahnke.