Picard Curves with Small Conductor

Michel Börner, Irene I. Bouw () and Stefan Wewers ()
Additional contact information
Michel Börner: Universität Ulm, Institut für Reine Mathematik
Irene I. Bouw: Universität Ulm, Institut für Reine Mathematik
Stefan Wewers: Universität Ulm, Institut für Reine Mathematik

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 97-122 from Springer

Abstract: Abstract We study the conductor of Picard curves over ℚ $$\mathbb {Q}$$ , which is a product of local factors. Our results are based on previous results on stable reduction of superelliptic curves that allow one to compute the conductor exponent f p at the primes p of bad reduction. A careful analysis of the possibilities of the stable reduction at p yields restrictions on the conductor exponent f p . We prove that Picard curves over ℚ $$\mathbb {Q}$$ always have bad reduction at p = 3, with f 3 ≥ 4. As an application we discuss the question of finding Picard curves with small conductor.

Keywords: Picard curves; Conductor; Semistable reduction; Primary 14H25. Secondary: 11G30; 14H45 (search for similar items in EconPapers)
Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_4

Ordering information: This item can be ordered from
http://www.springer.com/9783319705668

DOI: 10.1007/978-3-319-70566-8_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().