Rankin–Eisenstein classes and explicit reciprocity laws

We construct three-variable p-adic families of Galois cohomology classes attached to Rankin convolutions of modular forms, and prove an explicit reciprocity law relating these classes to critical values of L-functions. As a consequence, we prove finiteness results for the Selmer group of an elliptic curve twisted by a 2-dimensional odd irreducible Artin representation when the associated L-value does not vanish

Brevenal Inhibits Pacific Ciguatoxin-1B-Induced Neurosecretion from Bovine Chromaffin Cells

Ciguatoxins and brevetoxins are neurotoxic cyclic polyether compounds produced by dinoflagellates, which are responsible for ciguatera and neurotoxic shellfish poisoning (NSP) respectively. Recently, brevenal, a natural compound was found to specifically inhibit brevetoxin action and to have a beneficial effect in NSP. Considering that brevetoxin and ciguatoxin specifically activate voltage-sensitive Na+ channels through the same binding site, brevenal has therefore a good potential for the treatment of ciguatera. Pacific ciguatoxin-1B (P-CTX-1B) activates voltage-sensitive Na+ channels and promotes an increase in neurotransmitter release believed to underpin the symptoms associated with ciguatera. However, the mechanism through which slow Na+ influx promotes neurosecretion is not fully understood. In the present study, we used chromaffin cells as a model to reconstitute the sequence of events culminating in ciguatoxin-evoked neurosecretion. We show that P-CTX-1B induces a tetrodotoxin-sensitive rise in intracellular Na+, closely followed by an increase in cytosolic Ca2+ responsible for promoting SNARE-dependent catecholamine secretion. Our results reveal that brevenal and β-naphtoyl-brevetoxin prevent P-CTX-1B secretagogue activity without affecting nicotine or barium-induced catecholamine secretion. Brevenal is therefore a potent inhibitor of ciguatoxin-induced neurotoxic effect and a potential treatment for ciguatera

Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions

Let E/Q be an elliptic curve, p > 3 a good ordinary prime for E, and K∞ a p-adic Lie extension of a number field k. Under some standard hypotheses, we study the asymptotic growth in both the Mordell–Weil rank and Shafarevich–Tate group for E over a tower of extensions K ₙ/ₖ inside K∞; we obtain lower bounds on the former, and upper bounds on the latter’s size