Research

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My primary research interest is in Non Archimedean Geometry more specifically the perfectoid spaces. In particular I show how one can do Algebraic Geometry over these spaces. For example, I have constructed line bundles $\mathcal{O}(d)$ where $d\in\ds{Z}[1/p]$ instead of just $\ds{Z}$ (the case for algebraic geometry) and shown that the corresponding cohomology groups are infinite dimensional. Differential forms, Cartier and Weil Divisors are also defined and theorems corresponding to algebraic geometry are proven.