English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove an inequality between the conductor and the discriminant for allhyperelliptic curves defined over discretely valued fields $K$ with perfectresidue field of characteristic not 2. Specifically, if such a curve is givenby $y^2 = f(x)$ with $f(x) \in \mathcal{O}_K[x]$, and if $X$ is its minimalregular model over $\mathcal{O}_K$, then the negative of the Artin conductor of$X$ (and thus also the number of irreducible components of the special fiber of$X$) is bounded above by the valuation of disc$(f)$. There are no restrictionson genus of the curve or on the ramification of the splitting field of $f$.This generalizes earlier work of Ogg, Saito, Liu, and the second author.

Conductor-discriminant inequality for hyperelliptic curves in odd residue characteristic