Motives for modular forms

On the Bloch–Kato conjecture for elliptic modular forms of square-free level

“…We assume that ρ f,λ irreducible. Set E = E 0,λ and let O be the ring of integers of E. Let V be the premotivic structure defined over Q with coefficients in E 0 attached to our newform f ∈ S 2κ−2 (Γ 0 (M )) as in [34] and let V = V(κ). Let Σ ′ = {p|M } and Σ a finite set of places containing Σ ′ ∪ {ℓ}.…”

Siegel Modular Forms and Their Applications

“…In fact a good notation for writing this relation is (A better interpretation is as a relation in a suitable K-group and with S[2k + 2] as the motive associated to S 2k+2 . This motive can be constructed in the kth power of E as done by Scholl [86] or using moduli space of n-pointed elliptic curves as done by Consani and Faber,[17].) This 1 in the formula…”

Darmon cycles and the Kohnen-Shintani lifting

“…Note that for Type II discriminants D, we have w(f k 0 , D * ) = −1 and hence Let V N p p be the base change to Q p of the p-adic Galois reprsentation of [35]. For L any number field, let…”