Fibre products of elliptic surfaces

2006 ◽  
Vol 49 (2) ◽  
pp. 296-312 ◽  
Author(s):  
Matthias Schütt

AbstractThis 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.


2011 ◽  
Vol 200 (3) ◽  
pp. 1023-1050 ◽  
Author(s):  
Marta Lewicka ◽  
Maria Giovanna Mora ◽  
Mohammad Reza Pakzad

2018 ◽  
Vol 69 (3) ◽  
pp. 835-854 ◽  
Author(s):  
Dessislava H Kochloukova ◽  
Francismar Ferreira Lima

Dietary Fibre ◽  
2005 ◽  
pp. 350-354
Author(s):  
E. Del Toma ◽  
A. Clementi ◽  
C. Lintas ◽  
G. Quaglia

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