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

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 December 23, 2024, https://urss.warwick.ac.uk/items/show/584.