Geometry of Projective Perfectoid and Integer Partitions

Abstract

Line bundles of rational degree are defined using Perfectoid spaces, and their co-homology computed via standard Čech complex along with Kunneth formula. A new concept of `braided dimension' is introduced, which helps convert the curse of infinite dimensionality into a boon, which is then used to do Bezout type computations, define euler characters, describe ampleness and link integer partitions with geometry. This new concept of 'Braided dimension' gives a space within a space within a space an infinite tower of spaces, all intricately braided into each other. Finally, the concept of Blow Up over perfectoid space is introduced.