Exploring p-adic numbers, quotient groups, and jacobian varieties. Determining the genus and primes of good reduction for hyperelliptic curves using colemans theorem and sagemath
Title
Exploring p-adic numbers, quotient groups, and jacobian varieties. Determining the genus and primes of good reduction for hyperelliptic curves using colemans theorem and sagemath
Subject
Statistics
Creator
Zacharias Christodoulou
Date
2024
Contributor
Zacharias Christodoulou, Dr Horatio Boedihardjo, URSS
Abstract
This paper investigates the relationship between Jacobian varieties, hyperelliptic curve, and, p-adic numbers through the application of Coleman’s theorem. The study aims to determine the genus and identify primes of good reduction, which are crucial for understanding the number of rational solutions on these curves. Additionally, the paper demonstrates the practical application of these calculations using SageMath, highlighting its effectiveness in solving complex algebraic problems.
Files
Collection
Citation
Zacharias, “Exploring p-adic numbers, quotient groups, and jacobian varieties. Determining the genus and primes of good reduction for hyperelliptic curves using colemans theorem and sagemath,” URSS SHOWCASE, accessed October 16, 2024, https://urss.warwick.ac.uk/items/show/584.