Global quadratic units and Hecke algebras

  • Haruzo Hida

    Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA
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Abstract

Let {ρ\gothp}\gothp\{\rho_{\goth p}\}_{\goth p} be a compatible system of two dimansional \gothp{\goth p}--adic Galois representations attached to a cusp form of Neben type (D)(D>0)\left({D\over }\right) (D>0). We shall give an exact criterion, in terms of the fundamental unit ε\varepsilon of Q(D){\Bbb Q}(\sqrt{D}), determining primes \gothp{\goth p} for which the image of ρ\gothpmod\gothp\rho_{\goth p}\mod{\goth p} is dihedral. Then we shall state a conjecture which gives an explicit description of the universal pp--ordinary deformation ring of such mod \gothp{\goth p} dihedral representations.

Cite this article

Haruzo Hida, Global quadratic units and Hecke algebras. Doc. Math. 3 (1998), pp. 273–284

DOI 10.4171/DM/44