On abelian surfaces with potential quaternionic multiplication
Dieulefait, Luis V. ; Rotger, Victor
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 617-624 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
An abelian surface $A$ over a field $K$ has potential quaternionic multiplication if the ring $\End _{\bar K}(A)$ of geometric endomorphisms of $A$ is an order in an indefinite rational division quaternion algebra. In this brief note, we study the possible structures of the ring of endomorphisms of these surfaces and we provide explicit examples of Jacobians of curves of genus two which show that our result is sharp.
Publié le : 2005-12-14
Classification:  Abelian surface,  Galois representation,  quaternion algebra,  modularity,  11G18,  14G35 
@article{1133793348,
     author = {Dieulefait, Luis V. and Rotger, Victor},
     title = {On abelian surfaces with potential quaternionic multiplication},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 617-624},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1133793348}
}

Dieulefait, Luis V.; Rotger, Victor. On abelian surfaces with potential quaternionic multiplication. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  617-624. http://gdmltest.u-ga.fr/item/1133793348/