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)

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10.1093/qmath/has012

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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.",

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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.

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

Abstract

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