TL;DR
This paper introduces the perfectoid Tate curve, extending classical elliptic curve theory into the perfectoid setting, with new constructions of cohomology, theta functions, and series.
Contribution
It constructs the perfectoid Tate curve and develops its cohomology, theta functions, and Weierstrass series, advancing perfectoid geometry and number theory.
Findings
Defined the perfectoid Tate curve and computed its cohomology.
Constructed perfectoid theta functions and Weierstrass series.
Proved perfectoid versions of Abel-Jacobi and Riemann-Roch theorems.
Abstract
Perfectoid versions of Abel Jacobi and Reimann Roch Theorem are proved, and perfectoid Elliptic Curve is constructed. A Perfectoid Tate Curve is defined and its cohomology computed via a \v{C}ech complex. Furthermore, perfectoid Theta function and Weierstra{\ss} series are also defined and suitably interpreted.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Molecular spectroscopy and chirality