Tag Archives: Hida

Counting solutions to a_p = λ

We know that the eigenvalue of on is Are there any other level one cusp forms with the same Hecke eigenvalue? Maeda’s conjecture in its strongest form certainly implies that there does not. But what can one prove along these … Continue reading

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The nearly ordinary deformation ring is (usually) torsion over weight space

Let be an arbitrary number field. Let be a prime which splits completely in , and consider an absolutely irreducible representation: which is unramified outside finitely many primes. If one assumes that is geometric, then the Fontaine–Mazur conjecture predicts that … Continue reading

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The Thick Diagonal

Suppose that is an imaginary quadratic field. Suppose that is a cuspidal automorphic form for of cohomological type, and let us suppose that it contributes to the cohomology group for some congruence subgroup of . Choose a prime which splits … Continue reading

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