Period and index of genus one curves over number fields
Shahed Sharif

TL;DR
This paper constructs examples of genus one curves over number fields with specific prescribed period and index, advancing understanding of their arithmetic properties.
Contribution
It provides explicit constructions of genus one curves with given period and index over certain number fields, a novel achievement in arithmetic geometry.
Findings
Examples of genus one curves with prescribed period and index
Explicit constructions over specific number fields
Enhanced understanding of the relationship between period and index
Abstract
The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and index over certain number fields.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Cryptography and Residue Arithmetic · Coding theory and cryptography
