Details
| Original language | English |
|---|---|
| Pages (from-to) | 296-312 |
| Number of pages | 17 |
| Journal | Canadian mathematical bulletin |
| Volume | 49 |
| Issue number | 2 |
| Publication status | Published - Jun 2006 |
Abstract
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Canadian mathematical bulletin, Vol. 49, No. 2, 06.2006, p. 296-312.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the modularity of three Calabi-Yau threefolds with bad reduction at 11
AU - Schütt, Matthias
PY - 2006/6
Y1 - 2006/6
N2 - This paper investigates the modularity of three non-rigid Calabi-Yau threefolds with bad reduction at 11. They are constructed as fibre products of rational elliptic surfaces, involving the modular elliptic surface of level 5. Their middle ℓ-adic cohomology groups are shown to split into two-dimensional pieces, all but one of which can be interpreted in terms of elliptic curves. The remaining pieces are associated to newforms of weight 4 and level 22 or 55, respectively. For this purpose, we develop a method by Serre to compare the corresponding two-dimensional 2-adic Galois representations with uneven trace. Eventually this method is also applied to a self fibre product of the Hesse-pencil, relating it to a newform of weight 4 and level 27.
AB - This paper investigates the modularity of three non-rigid Calabi-Yau threefolds with bad reduction at 11. They are constructed as fibre products of rational elliptic surfaces, involving the modular elliptic surface of level 5. Their middle ℓ-adic cohomology groups are shown to split into two-dimensional pieces, all but one of which can be interpreted in terms of elliptic curves. The remaining pieces are associated to newforms of weight 4 and level 22 or 55, respectively. For this purpose, we develop a method by Serre to compare the corresponding two-dimensional 2-adic Galois representations with uneven trace. Eventually this method is also applied to a self fibre product of the Hesse-pencil, relating it to a newform of weight 4 and level 27.
UR - http://www.scopus.com/inward/record.url?scp=33745258402&partnerID=8YFLogxK
UR - https://arxiv.org/pdf/math/0405450.pdf
U2 - 10.4153/CMB-2006-031-9
DO - 10.4153/CMB-2006-031-9
M3 - Article
AN - SCOPUS:33745258402
VL - 49
SP - 296
EP - 312
JO - Canadian mathematical bulletin
JF - Canadian mathematical bulletin
SN - 0008-4395
IS - 2
ER -