dc.creator | Pacetti, Ariel Martín | |
dc.date.accessioned | 2021-02-17T13:47:59Z | |
dc.date.accessioned | 2022-10-15T01:33:33Z | |
dc.date.available | 2021-02-17T13:47:59Z | |
dc.date.available | 2022-10-15T01:33:33Z | |
dc.date.created | 2021-02-17T13:47:59Z | |
dc.date.issued | 2007-12 | |
dc.identifier | Pacetti, Ariel Martín; On the embedding problem for 2+s4 representations; American Mathematical Society; Mathematics of Computation; 74; 260; 12-2007; 2063-2075 | |
dc.identifier | 0025-5718 | |
dc.identifier | http://hdl.handle.net/11336/125780 | |
dc.identifier | CONICET Digital | |
dc.identifier | CONICET | |
dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/4330426 | |
dc.description.abstract | Let 2+S4 denote the double cover of S4 corresponding to the element in H2(S4, Z/2Z) where transpositions lift to elements of order 2 and the product of two disjoint transpositions to elements of order 4. Given an elliptic curve E, let E[2] denote its 2-torsion points. Under some conditions on E elements in H1(GalQ, E[2])\{0} correspond to Galois extensions N of Q with Galois group (isomorphic to) S4. In this work we give an interpretation of the addition law on such fields, and prove that the obstruction for N having a Galois extension N˜ with Gal(N/˜ Q) 2+S4 gives a homomorphism s+ 4 : H1(GalQ, E[2]) → H2(GalQ, Z/2Z). As a corollary we can prove (if E has conductor divisible by few primes and high rank) the existence of 2-dimensional representations of the absolute Galois group of Q attached to E and use them in some examples to construct 3/2 modular forms mapping via the Shimura map to (the modular form of weight 2 attached to) E. | |
dc.language | eng | |
dc.publisher | American Mathematical Society | |
dc.relation | info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1090/S0025-5718-07-01940-0 | |
dc.rights | https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ | |
dc.rights | info:eu-repo/semantics/restrictedAccess | |
dc.subject | Galois representations | |
dc.subject | Shimura correspondence | |
dc.title | On the embedding problem for 2+s4 representations | |
dc.type | info:eu-repo/semantics/article | |
dc.type | info:ar-repo/semantics/artículo | |
dc.type | info:eu-repo/semantics/publishedVersion | |