Universität zu Köln

Loebrich, Steffen (2017). A Gap in the Spectrum of the Faltings Height. J. Theor. Nr. Bordx., 29 (1). S. 289 - 306. TALENCE: UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX. ISSN 1246-7405

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Loebrich, Steffen UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-246608
Journal or Publication Title:	J. Theor. Nr. Bordx.
Volume:	29
Number:	1
Page Range:	S. 289 - 306
Date:	2017
Publisher:	UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX
Place of Publication:	TALENCE
ISSN:	1246-7405
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language VARIETIES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/24660