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Abstract: We introduce the formalism of Coleman''s power series for rank 1 Drinfeld modules and apply it to formulate and prove the analogue of Wiles'' explicit reciprocity law in this setting. [Copyright &y& Elsevier]

Let F be a global function field of characteristic p and E/F an elliptic curve with split multiplicative reduction at the place ∞: then E can be obtained as a factor of the Jacobian of some Drinfeld modular curve. This fact is used to associate to E a measure μE on P1(F∞). By choosing an appropriate embedding of a quadratic unramified extension K/F into the matrix algebra M2(F), μE is pushed forward to a measure on a p-adic group G, isomorphic to an anticyclotomic Galois group over the Hilbert class field of K. Integration on G then yields a Heegner point on E when ∞ is inert in K and an analogue of the L-invariant if ∞ is split. In the last section, the same methods are extended to integration on a geometric cyclotomic Galois group. [Copyright &y& Elsevier]

Let A be an abelian variety defined over a global field F of positive characteristic p and let F / F be a Z p N -extension, unramified outside a finite set of places of F . Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the p -primary Selmer group of A . To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Z p d -extension F d / F and for any Z p d − 1 -extension contained in F d , and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Z p [ [ Gal ( F / F ) ] ] in the case A is a constant abelian variety. [ABSTRACT FROM AUTHOR]