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Explore a nonstandard approach to almost mathematics through this mathematical lecture that presents innovative methods using ultraproducts to transform "almost" properties into genuine mathematical properties. Delve into the technical toolkit of almost mathematics, originally introduced by Faltings and developed by Gabber–Ramero, which plays a central role in commutative algebra and modern p-adic geometry. Learn about the nonstandard approach based on ultraproducts, a method that originated with Gabber and was independently rediscovered by Jahnke and the speaker. Discover how this approach provides new perspectives on almost mathematical concepts and examine a nonstandard version of the almost purity theorem. The presentation represents joint work in progress with Franziska Jahnke, offering insights into cutting-edge research at the intersection of nonstandard analysis and algebraic geometry.
