Details
| Original language | English |
|---|---|
| Pages (from-to) | 8485-8524 |
| Number of pages | 40 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 373 |
| Issue number | 12 |
| Early online date | 29 Sept 2020 |
| Publication status | Published - Dec 2020 |
Abstract
We introduce the split torsor method to count rational points of bounded height on Fano varieties. As an application, we prove Manin's conjecture for all nonsplit quartic del Pezzo surfaces of type A 3 + A 1 over arbitrary number fields. The counting problem on the split torsor is solved in the framework of o-minimal structures.
Keywords
- math.NT, math.AG, 11D45 (Primary) 11G35, 14G05 (Secondary)
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics(all)
- Applied Mathematics
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In: Transactions of the American Mathematical Society, Vol. 373, No. 12, 12.2020, p. 8485-8524.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The split torsor method for Manin's conjecture
AU - Derenthal, Ulrich
AU - Pieropan, Marta
N1 - Funding Information: Received by the editors July 22, 2019, and, in revised form, February 5, 2020. 2010 Mathematics Subject Classification. Primary 11D45; Secondary 11G35, 14G05. The first author was partly supported by grant DE 1646/4-2 of the Deutsche Forschungsge-meinschaft. Some of this work was done while he was on sabbatical leave at the University of Oxford. The second author was partly supported by grant ES 60/10-1 of the Deutsche Forschungsgemeinschaft.
PY - 2020/12
Y1 - 2020/12
N2 - We introduce the split torsor method to count rational points of bounded height on Fano varieties. As an application, we prove Manin's conjecture for all nonsplit quartic del Pezzo surfaces of type A 3 + A 1 over arbitrary number fields. The counting problem on the split torsor is solved in the framework of o-minimal structures.
AB - We introduce the split torsor method to count rational points of bounded height on Fano varieties. As an application, we prove Manin's conjecture for all nonsplit quartic del Pezzo surfaces of type A 3 + A 1 over arbitrary number fields. The counting problem on the split torsor is solved in the framework of o-minimal structures.
KW - math.NT
KW - math.AG
KW - 11D45 (Primary) 11G35, 14G05 (Secondary)
UR - http://www.scopus.com/inward/record.url?scp=85096703056&partnerID=8YFLogxK
U2 - 10.1090/tran/8133
DO - 10.1090/tran/8133
M3 - Article
VL - 373
SP - 8485
EP - 8524
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 12
ER -