A MANIN-MUMFORD THEOREM FOR THE MAXIMAL COMPACT SUBGROUP OF A UNIVERSAL VECTORIAL EXTENSION OF A PRODUCT OF ELLIPTIC CURVESCitation formats

Standard

A MANIN-MUMFORD THEOREM FOR THE MAXIMAL COMPACT SUBGROUP OF A UNIVERSAL VECTORIAL EXTENSION OF A PRODUCT OF ELLIPTIC CURVES. / Jones, Gareth; Schmidt, Harry.

In: International Mathematics Research Notices, Vol. 0, rnz207, 20.11.2019.

Research output: Contribution to journalArticlepeer-review

Harvard

APA

Vancouver

Author

Bibtex

@article{ea71ca73fc2c4f9890a506832648dd60,
title = "A MANIN-MUMFORD THEOREM FOR THE MAXIMAL COMPACT SUBGROUP OF A UNIVERSAL VECTORIAL EXTENSION OF A PRODUCT OF ELLIPTIC CURVES",
abstract = "We study the intersection of an algebraic variety with the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves. For this intersection we show a Manin- Mumford type statement. This answers some questions posed by Corvaja-Masser-Zannier which arose in connection with their investigation of the intersection of an algebraic curve with the maximal compact subgroup of various algebraic groups. In particular they proved that these intersections are finite for universal vectorial extensions of elliptic curves. Using Khovanskii{\textquoteright}s zero-estimates combined with a stratification result of Gabrielov-Vorobjov and recent work of the authors, we obtain effective bounds for this intersection that only depend on the degree of the algebraic variety and the dimension of the group. As a corollary, we obtain new uniform results of Manin-Mumford type for additive extensions of certain abelian varieties.",
author = "Gareth Jones and Harry Schmidt",
year = "2019",
month = nov,
day = "20",
doi = "10.1093/imrn/rnz207",
language = "English",
volume = "0",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",

}

RIS

TY - JOUR

T1 - A MANIN-MUMFORD THEOREM FOR THE MAXIMAL COMPACT SUBGROUP OF A UNIVERSAL VECTORIAL EXTENSION OF A PRODUCT OF ELLIPTIC CURVES

AU - Jones, Gareth

AU - Schmidt, Harry

PY - 2019/11/20

Y1 - 2019/11/20

N2 - We study the intersection of an algebraic variety with the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves. For this intersection we show a Manin- Mumford type statement. This answers some questions posed by Corvaja-Masser-Zannier which arose in connection with their investigation of the intersection of an algebraic curve with the maximal compact subgroup of various algebraic groups. In particular they proved that these intersections are finite for universal vectorial extensions of elliptic curves. Using Khovanskii’s zero-estimates combined with a stratification result of Gabrielov-Vorobjov and recent work of the authors, we obtain effective bounds for this intersection that only depend on the degree of the algebraic variety and the dimension of the group. As a corollary, we obtain new uniform results of Manin-Mumford type for additive extensions of certain abelian varieties.

AB - We study the intersection of an algebraic variety with the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves. For this intersection we show a Manin- Mumford type statement. This answers some questions posed by Corvaja-Masser-Zannier which arose in connection with their investigation of the intersection of an algebraic curve with the maximal compact subgroup of various algebraic groups. In particular they proved that these intersections are finite for universal vectorial extensions of elliptic curves. Using Khovanskii’s zero-estimates combined with a stratification result of Gabrielov-Vorobjov and recent work of the authors, we obtain effective bounds for this intersection that only depend on the degree of the algebraic variety and the dimension of the group. As a corollary, we obtain new uniform results of Manin-Mumford type for additive extensions of certain abelian varieties.

U2 - 10.1093/imrn/rnz207

DO - 10.1093/imrn/rnz207

M3 - Article

VL - 0

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

M1 - rnz207

ER -