Bipartite Euler systems

If E is an elliptic curve over Q and K is an imaginary quadratic field, there is an Iwasawa main conjecture predicting the behavior of the Selmer group of E over the anticyclotomic Z_p-extension of K. The main conjecture takes different forms depending on the sign of the functional equation of L(E/K,s). In the present work we combine ideas of Bertolini and Darmon with those of Mazur and Rubin to shown that the main conjecture, regardless of the sign of the functional equation, can be reduced to proving the nonvanishing of sufficiently many p-adic L-functions attached to a family of congruent modular forms

Introduction (to Dossier on Walter Benjamin and Education)

Although it is well known that Walter Benjamin played a leading role in the antebellum German Youth Movement, withdrawing from the presidency of the Berlin Independent Students Association and from other reformist activities only with the onset of World War I, scholars often do not ask whether this multifaceted student activism had any effect on his later thought and writing. This dossier proposes to investigate the early writings on youth and educational reform and their discernible afterlife in the better known historical-materialist phase of Benjamin’s career, including his writings on radio, film, children’s literature, and children’s theater, as well as his studies of Franz Kafka and Bertolt Brecht. The introduction provides brief summaries of the ten articles comprising the dossier and their relation to one another, and it addresses the question of the relevance of Benjamin’s ideas on education to contemporary debates concerning pedagogy

Anticyclotomic Iwasawa theory of CM elliptic curves

We study the Iwasawa theory of a CM elliptic curve $E$ in the anticyclotomic $\mathbf{Z}_p$-extension of the CM field, where $p$ is a prime of good, ordinary reduction for $E$. When the complex $L$-function of $E$ vanishes to even order, the two variable main conjecture of Rubin implies that the Pontryagin dual of the $p$-power Selmer group over the anticyclotomic extension is a torsion Iwasawa module. When the order of vanishing is odd, work of Greenberg shows that it is not a torsion module. In this paper we show that in the case of odd order of vanishing the dual of the Selmer group has rank exactly one, and we prove a form of the Iwasawa main conjecture for the torsion submodule.Comment: Final version. To appear in the Annales de L'Institut Fourie