Details
Original language | English |
---|---|
Pages (from-to) | 47-79 |
Number of pages | 33 |
Journal | Israel journal of mathematics |
Volume | 210 |
Issue number | 1 |
Publication status | Published - 1 Sept 2015 |
Abstract
Given an extension of number fields E ⊂ F and a projective variety X over F, we compare the problem of counting the number of rational points of bounded height on X with that of its Weil restriction over E. In particular, we consider the compatibility with respect to the Weil restriction of conjectural asymptotic formulae due to Manin and others. Using our methods we prove several new cases of these conjectures. We also construct new counterexamples over every number field.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Israel journal of mathematics, Vol. 210, No. 1, 01.09.2015, p. 47-79.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Rational points of bounded height and the Weil restriction
AU - Loughran, Daniel
N1 - Publisher Copyright: © 2015, Hebrew University of Jerusalem. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - Given an extension of number fields E ⊂ F and a projective variety X over F, we compare the problem of counting the number of rational points of bounded height on X with that of its Weil restriction over E. In particular, we consider the compatibility with respect to the Weil restriction of conjectural asymptotic formulae due to Manin and others. Using our methods we prove several new cases of these conjectures. We also construct new counterexamples over every number field.
AB - Given an extension of number fields E ⊂ F and a projective variety X over F, we compare the problem of counting the number of rational points of bounded height on X with that of its Weil restriction over E. In particular, we consider the compatibility with respect to the Weil restriction of conjectural asymptotic formulae due to Manin and others. Using our methods we prove several new cases of these conjectures. We also construct new counterexamples over every number field.
UR - http://www.scopus.com/inward/record.url?scp=84945927594&partnerID=8YFLogxK
U2 - 10.1007/s11856-015-1245-x
DO - 10.1007/s11856-015-1245-x
M3 - Article
AN - SCOPUS:84945927594
VL - 210
SP - 47
EP - 79
JO - Israel journal of mathematics
JF - Israel journal of mathematics
SN - 0021-2172
IS - 1
ER -