Details
| Original language | English |
|---|---|
| Pages (from-to) | 1939-1963 |
| Number of pages | 25 |
| Journal | Journal of number theory |
| Volume | 130 |
| Issue number | 9 |
| Publication status | Published - Sept 2010 |
Abstract
Keywords
- Fermat surface, Néron-Severi group, Primary, Secondary, Supersingular reduction
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of number theory, Vol. 130, No. 9, 09.2010, p. 1939-1963.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Lines on Fermat surfaces
AU - Schütt, Matthias
AU - Shioda, Tetsuji
AU - van Luijk, Ronald
N1 - Funding information: Partial funding from DFG under grant Schu 2266/2-2 and JSPS under Grant-in-Aid for Scientific Research (C) No. 20540051 is gratefully acknowledged. * Corresponding author. E-mail addresses: schuett@math.uni-hannover.de (M. Schütt), shioda@rikkyo.ac.jp (T. Shioda), rvl@math.leidenuniv.nl (R. van Luijk). URLs: http://www.iag.uni-hannover.de/~schuett/ (M. Schütt), http://www.rkmath.rikkyo.ac.jp/math/shioda/ (T. Shioda), http://www.math.leidenuniv.nl/~rvl (R. van Luijk).
PY - 2010/9
Y1 - 2010/9
N2 - We prove that the Néron-Severi groups of several complex Fermat surfaces are generated by lines. Specifically, we obtain these new results for all degrees up to 100 that are relatively prime to 6. The proof uses reduction modulo a supersingular prime. The techniques are developed in detail. They can be applied to other surfaces and varieties as well.
AB - We prove that the Néron-Severi groups of several complex Fermat surfaces are generated by lines. Specifically, we obtain these new results for all degrees up to 100 that are relatively prime to 6. The proof uses reduction modulo a supersingular prime. The techniques are developed in detail. They can be applied to other surfaces and varieties as well.
KW - Fermat surface
KW - Néron-Severi group
KW - Primary
KW - Secondary
KW - Supersingular reduction
UR - http://www.scopus.com/inward/record.url?scp=77953692452&partnerID=8YFLogxK
UR - https://arxiv.org/abs/0812.2377
U2 - 10.1016/j.jnt.2010.01.008
DO - 10.1016/j.jnt.2010.01.008
M3 - Article
AN - SCOPUS:77953692452
VL - 130
SP - 1939
EP - 1963
JO - Journal of number theory
JF - Journal of number theory
SN - 0022-314X
IS - 9
ER -