Local Heights on Curves

Benedict H. Gross

Chapter Chapter XIV in Arithmetic Geometry, 1986, pp 327-339 from Springer

Abstract: Abstract In this paper we will review the theory of local heights on curves and describe its relationship to the global height pairing on the Jacobian. The local results are all special cases of Néron’s theory [9], [10]; the global pairing was discovered independently by Néron and Tate [5], We will also discuss extensions of the local pairing to divisors of arbitrary degree and to divisors which are not relatively prime. The first extension is due to Arakelov [1]; the second is implicit in Tate’s work on elliptic curves [12]. I have also included several sections of examples which illustrate the general theory.

Keywords: Elliptic Curf; Prime Divisor; Degree Zero; Local Pairing; Local Height (search for similar items in EconPapers)
Date: 1986
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:978-1-4613-8655-1_14

Ordering information: This item can be ordered from
http://www.springer.com/9781461386551

DOI: 10.1007/978-1-4613-8655-1_14

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 ().