Abstract
Let $C$ be a hyperelliptic curve of good reduction defined over a discrete valuation field $K$ with algebraically closed residue field $k$. Assume moreover that $\text{char\,} k\ne2$. Given $d\in K^*\setminus K^{*2}$, we introduce an explicit description of the minimal regular model of the quadratic twist of $C$ by $d$. As an application, we show that if $C/\q$ is a nonsingular hyperelliptic curve given by $y^2=f(x)$ with $f$ an irreducible polynomial, there exists a positive density family of prime quadratic twists of $C$ which are not everywhere locally soluble.
Citation
Mohammad Sadek. "On quadratic twists of hyperelliptic curves." Rocky Mountain J. Math. 44 (3) 1015 - 1026, 2014. https://doi.org/10.1216/RMJ-2014-44-3-1015
Information