Details
| Original language | English |
|---|---|
| Pages (from-to) | 1191-1225 |
| Number of pages | 35 |
| Journal | Mathematische Annalen |
| Volume | 368 |
| Issue number | 3-4 |
| Publication status | Published - 1 Aug 2017 |
Abstract
We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.
Keywords
- 11G35, 14C34, 14D23, 14J50, 14K30, 14M10
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Mathematische Annalen, Vol. 368, No. 3-4, 01.08.2017, p. 1191-1225.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Complete intersections
T2 - moduli, Torelli, and good reduction
AU - Javanpeykar, A.
AU - Loughran, D.
N1 - Funding information: We are grateful to Giuseppe Ancona, Jean-Benoît Bost, Martin Bright, Fréderic Campana, Jean-Louis Colliot-Thélène, Bas Edixhoven, Jochen Heinloth, Marc Hindry, David Holmes, Ben Moonen, Laurent Moret-Bailly, Duco van Straten, Lenny Taelman, Olivier Wittenberg, and Kang Zuo for helpful discussions on several parts of this paper. Special thanks go to Olivier Benoist for very helpful discussions on complete intersections and level structure, Yohan Brunebarbe for his help on period maps and the proof of Theorem , and Angelo Vistoli for answering our questions on stacks and his help in proving Proposition . We are very grateful to the anonymous referee for useful comments. The first named author gratefully acknowledges the support of SFB/Transregio 45.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.
AB - We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.
KW - 11G35
KW - 14C34
KW - 14D23
KW - 14J50
KW - 14K30
KW - 14M10
UR - http://www.scopus.com/inward/record.url?scp=84982902920&partnerID=8YFLogxK
U2 - 10.1007/s00208-016-1455-5
DO - 10.1007/s00208-016-1455-5
M3 - Article
AN - SCOPUS:84982902920
VL - 368
SP - 1191
EP - 1225
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 3-4
ER -