Experimental Indications of Three-dimensional Galois Representations from the Cohomology of SL(3, Z)
- 1 January 1992
- journal article
- research article
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 1 (3) , 209-223
- https://doi.org/10.1080/10586458.1992.10504259
Abstract
Conjecturally, any “algebraic” automorphic represent ation on GL(n) should have an n-d imensional Galois representation attached. Many examples of algebraic automorphic representations come from the cohomology over C of congruence subgroups of GL(n, Z). On the other hand, the first author has conjectured that for any Hecke eigenclass in the mod p cohomology of a congruence subgroup of GL(n Z) there should be In attached n-dimensional Galois representation. By computer, we found Heeke eigenclasses in the mod p co-homology of certain congruence subgroups of SL(3, Z). In a range of examples, we then found a Galois representation (uniquely determined up to isomorphism by our data) that seemed to be attac hed to the Hecke eigenclass.Keywords
This publication has 9 references indexed in Scilit:
- Galois representations attached to modp cohomology of GL(n,ℤ)Duke Mathematical Journal, 1992
- An $$\widehat{A_4 }$$ extension of ? attached to a non-selfdual automorphic form onGL(3)Mathematische Annalen, 1991
- Explicit construction of Ãn type fieldsJournal of Algebra, 1989
- Algorithmic Algebraic Number TheoryPublished by Cambridge University Press (CUP) ,1989
- Sur les représentations modulaires de degré 2 de Gal(Q¯/Q)Duke Mathematical Journal, 1987
- Computations of cuspidal cohomology of congruence subgroups of SL(3, Z)Journal of Number Theory, 1984
- L'invariant de Witt de la forme Tr(x 2)Commentarii Mathematici Helvetici, 1984
- Icosahedral Galois RepresentationsPublished by Springer Nature ,1978
- Determination of the ordinary and modular ternary linear groupsTransactions of the American Mathematical Society, 1911