@article{a43b97361f31497989e6a1e98f5000bb,

title = "Modular representations of GL(3, Fp), symmetric squares, and mod-p cohomology of GL(3, Z)",

abstract = "We prove certain cases of nonabelian reciprocity between mod p Galois representations and Hecke eigenclasses in the mod p cohomology of GL(3,Z), using the symmetric square liftings from GL(2) and congruences on Hecke eigenvalues. We need to develop some modular representation theory for GL(3,Z/p). In some cases we also need to invoke certain computer calculations to finish the proof.",

keywords = "Galois representations, Mod-p cohomology",

author = "Avner Ash and Tiep, {Pham Huu}",

note = "Funding Information: * The first author was supported in part by NSA Grant MDA-904-94-2030 and NSF Grant DMS-9531675. †Part of this work was done while the second author was participating in the special semester on Representations of Algebraic Groups and Related Finite Groups at the Isaac Newton Institute (Cambridge). It is a pleasure to thank the Institute for its hospitality. ‡The authors are grateful to S. Doty, R. Taylor, G. Walker, and B. Mazur for helpful discussions.",

year = "1999",

month = dec,

day = "15",

doi = "10.1006/jabr.1999.7988",

language = "English (US)",

volume = "222",

pages = "376--399",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "2",

}