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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the minimal resultant divisor of self-maps of the projective lineover a number field or a function field and its relation to the conductor. Theguiding focus is the exploration of a dynamical analog to Theorem 1.1, whichbounds the degree of the minimal discriminant of an elliptic surface in termsof the conductor. We study minimality and semi-stability, considering whatconditions imply minimality (Theorem 4.4) and whether semi-stable models andpresentations are minimal, proving results in the degree two case (Theorems4.6, 4.7). We prove the singular reduction of a semi-stable presentationcoincides with the bad reduction (Theorem 3.1). Given an elliptic curve over afunction field with semi-stable bad reduction, we show the associated Lattesmap has unstable bad reduction (Theorem 3.6). Degree 2 maps in normal form withsemi-stable bad reduction are used to construct a counterexample (Theorem 2.1)to a natural dynamical analog to Theorem 1.1. Finally, we consider the notionof "critical bad reduction," and show that a dynamical analog to Theorem 1.1may still be possible using the locus of critical bad reduction to define theconductor (Theorem 4.10, Theorem 4.13).

Resultant and conductor of geometrically semi-stable self maps of the projective line over a number field or function field