The explicit calculation of čech cohomology and an extension of Davenport's inequality

Ran Tian

doi:10.1093/qmath/has012

The explicit calculation of čech cohomology and an extension of Davenport's inequality

Ran Tian

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We extend Davenport's inequality to general elliptic curves over (t) written in Weierstrass forms. The obtained result is an effective version of a result by Voloch, and also improves a bound given by Hindry-Silverman. The method depends on an explicit calculation of the Čech cohomology of sheaves of differentials on an elliptic surface.

Original language	English
Pages (from-to)	591-618
Number of pages	28
Journal	Quarterly Journal of Mathematics
Volume	64
Issue number	2
DOIs	https://doi.org/10.1093/qmath/has012
Publication status	Published - 2013 Jun 1

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1093/qmath/has012

Fingerprint Dive into the research topics of 'The explicit calculation of čech cohomology and an extension of Davenport's inequality'. Together they form a unique fingerprint.

Cite this

@article{e2f2c63161fc4d828fc73d4c1fef3d13,

title = "The explicit calculation of {\v c}ech cohomology and an extension of Davenport's inequality",

abstract = "We extend Davenport's inequality to general elliptic curves over (t) written in Weierstrass forms. The obtained result is an effective version of a result by Voloch, and also improves a bound given by Hindry-Silverman. The method depends on an explicit calculation of the {\v C}ech cohomology of sheaves of differentials on an elliptic surface.",

author = "Ran Tian",

year = "2013",

month = jun,

day = "1",

doi = "10.1093/qmath/has012",

language = "English",

volume = "64",

pages = "591--618",

journal = "Quarterly Journal of Mathematics",

issn = "0033-5606",

publisher = "Oxford University Press",

number = "2",

}

TY - JOUR

T1 - The explicit calculation of čech cohomology and an extension of Davenport's inequality

AU - Tian, Ran

PY - 2013/6/1

Y1 - 2013/6/1

N2 - We extend Davenport's inequality to general elliptic curves over (t) written in Weierstrass forms. The obtained result is an effective version of a result by Voloch, and also improves a bound given by Hindry-Silverman. The method depends on an explicit calculation of the Čech cohomology of sheaves of differentials on an elliptic surface.

AB - We extend Davenport's inequality to general elliptic curves over (t) written in Weierstrass forms. The obtained result is an effective version of a result by Voloch, and also improves a bound given by Hindry-Silverman. The method depends on an explicit calculation of the Čech cohomology of sheaves of differentials on an elliptic surface.

UR - http://www.scopus.com/inward/record.url?scp=84877992238&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877992238&partnerID=8YFLogxK

U2 - 10.1093/qmath/has012

DO - 10.1093/qmath/has012

M3 - Article

AN - SCOPUS:84877992238

VL - 64

SP - 591

EP - 618

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 2

ER -