Yoshida lifts and the Bloch–Kato conjecture for the convolution L-function
نویسنده
چکیده
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 special value of the convolution L-function of f1 and f2). We achieve this by constructing congruences between the Yoshida lift Y (f1 ⊗ f2) of f1 and f2 and Siegel modular forms whose p-adic Galois representations are irreducible. Our result is conditional upon a conjectural formula for the Petersson norm of Y (f1 ⊗ f2).
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