Geometry of Projective Perfectoid and Integer Partitions

TL;DR

This paper introduces the concept of braided dimension in perfectoid spaces, linking integer partitions with geometry, and develops new tools for cohomology, ampleness, and blow-ups in this context.

Contribution

It proposes the novel concept of braided dimension in perfectoid spaces, enabling new geometric and algebraic computations involving integer partitions.

Findings

Defined line bundles of rational degree using perfectoid spaces

Introduced the concept of braided dimension to handle infinite dimensionality

Linked integer partitions with geometric structures

Abstract

Line bundles of rational degree are defined using Perfectoid spaces, and their co-homology computed via standard \v{C}ech 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.