L-Functions and Tamagawa Numbers of Motives

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The unipotent Albanese map and Selmer varieties for curves (2005, methodology): “There is are maps from K-theory ([3], section 5)”
Analytic families of finite-slope Selmer groups (2013, methodology): “The remedy for this is likely to be the use of Euler–Poincaré formulas to construct integral isogeny invariants, following [Bloch and Kato 1990; Fontaine and Perrin-Riou 1994; Perrin-Riou 2000].”
A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves (2012, background): “ a base point b∈X(Z). Then the associated map jp: X(Zp) →H1f(Gp,U1) can be identiﬁed with the map X(Zp) ⊂X(Qp) →JX(Qp) →TeJX, where JX is the Jacobian of Xand TeJX is its tangent space at the origin [BK]. 7.2. If we assume that ШJ X [p∞] <∞, then it follows that JX(Z) ⊗Qp= Sel1(X). Indeed, the co”
Cohomology and Duality for (φ, Γ)-modules over the Robba Ring (2007, methodology): “This would extend the work of Bloch-Kato for ordinary representations [6].”
On the Equivariant Tamagawa Number Conjecture for Tate Motives, Part II. (2006, methodology): “This map is bijective (since r > 0) and H1 f(Kp, Qp(r)) coincides with ˆ O× Kp for r = 1 and with H 1 (Kp, Qp(r)) for r > 1 (cf. [ 5 ]). Also, both”