A Gap in the Spectrum of the Faltings Height

2015/05/04 by Steffen Löbrich, Löbrich, Steffen
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1505.00602

arxiv created 2015/12/16 · arxiv updated 2015/12/17

Abstract

We show that the minimum h_min of the stable Faltings height on elliptic curves found by Deligne is followed by a gap. This means that there is a constant C >0 such that for every elliptic curve E/K with everywhere semistable reduction over a number field K, we either have h(E/K)=h_min or h(E/K)≥ h_min +C. We determine such an absolute constant explicitly. On the contrary, we show that there is no such gap for elliptic curves with unstable reduction.

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