On the Bloch-kato Conjecture for Elliptic Modular Forms of Square-free Level
نویسنده
چکیده
Let κ ≥ 6 be an even integer, M an odd square-free integer, and f ∈ S2κ−2(Γ0(M)) a newform. We prove that under some reasonable assumptions that half of the λ-part of the Bloch-Kato conjecture for the near central critical value L(κ, f) is true. We do this by bounding the l-valuation of the order of the appropriate Bloch-Kato Selmer group below by the l-valuation of algebraic part of L(κ, f). We prove this by constructing a congruence between the Saito-Kurokawa lift of f and a cuspidal Siegel modular form.
منابع مشابه
Computational Evidence for the Bloch-kato Conjecture for Elliptic Modular Forms of Square-free Level
In this short note we provide computational evidence for the main result found in On the Bloch-Kato conjecture for elliptic modular forms of square-free level.
متن کاملYoshida lifts and the Bloch–Kato conjecture for the convolution L-function
Let f1 (resp. f2) denote two (elliptic) newforms of prime level N , trivial character and weight 2 (resp. k + 2, where k ∈ {8, 12}). We provide evidence for the Bloch-Kato conjecture for the motive M = ρf1⊗ρf2 (−k/2−1) by proving that under some assumptions the p-valuation of the order of the Bloch-Kato Selmer group of M is bounded from below by the p-valuation of the relevant L-value (a specia...
متن کاملOn the Bloch-Kato conjecture for adjoint L-functions of modular forms
This paper concerns the Tamagawa number conjecture of Bloch and Kato [B-K] for adjoint motives of modular forms of weight k ≥ 2. The conjecture relates the value at 0 of the associated L-function to arithmetic invariants of the motive. We prove that it holds up to powers of certain “bad primes.” The strategy for achieving this is essentially due to Wiles [Wi], as completed with Taylor in [T-W]....
متن کاملThe Bloch-kato Conjecture for Adjoint Motives of Modular Forms (to Appear in Math. Res. Letters)
The Tamagawa number conjecture of Bloch and Kato describes the behavior at integers of the L-function associated to a motive over Q. Let f be a newform of weight k ≥ 2, level N with coefficients in a number field K. Let M be the motive associated to f and let A be the adjoint motive of M . Let λ be a finite prime of K. We verify the λ-part of the Bloch-Kato conjecture for L(A, 0) and L(A, 1) wh...
متن کاملSupersingular Locus of Hilbert Modular Varieties, Arithmetic Level Raising, and Selmer Groups
This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus to all Shimura varieties given by totally indefinite quaternion algebras over totally real number fields. Second, we generalize the result of Ribet on arithmetic level raising to such Shimura varieties in the inert case. Third, as an application to number theory, we ...
متن کامل