Lifting units modulo exchange ideals and C*-algebras with real rank zero

Given a unital ring $R$ and a two-sided ideal $I$ of $R$, we consider the question of determining when a unit of $R/I$ can be lifted to a unit of $R$. For the wide class of separative exchange ideals $I$, we show that the only obstruction to lifting invertibles relies on a K-theoretic condition on $I$. This allows to extend previously known index theories to this context. Using this we can draw consequences for von Neumann regular rings and C*-algebras with real rank zero.Comment: 11 pages; to appear in Journal fur die Reine und Angewandte Mathemati

On the pp-adic variation of Heegner points

In this paper, we prove an "explicit reciprocity law" relating Howard's system of big Heegner points to a two-variable $p$-adic $L$-function (constructed here) interpolating the $p$-adic Rankin $L$-series of Bertolini-Darmon-Prasanna in Hida families. As applications, we obtain a direct relation between classical Heegner cycles and the higher weight specializations of big Heegner points, refining earlier work of the author, and prove the vanishing of Selmer groups of CM elliptic curves twisted by 2-dimensional Artin representations in cases predicted by the equivariant Birch and Swinnerton-Dyer conjecture.Comment: 26 page

An Experiment on Learning Appropriate Selectional Restrictions from a Parsed Corpus

We present a methodology to extract Selectional Restrictions at a variable level of abstraction from phrasally analyzed corpora. The method relays in the use of a wide-coverage noun taxonomy and a statistical measure of the co-occurrence of linguistic items. Some experimental results about the performance of the method are provided.Comment: 11 page

On Reidys and Stadler's metrics for RNA secondary structures

We compute explicitly several abstract metrics for RNA secondary structures defined by Reidys and Stadler.Comment: 6 page

Cosmological acceleration from a gas of strings

In string gas cosmology, the extra dimensions of the underlying theory are kept at a microscopic scale by a gas of strings. In the matter-dominated era, however, dust pressure can lead to oscillations of the extra dimensions and to acceleration in the three visible dimensions, even with a vanishing cosmological term. We review the resulting oscillating expansion history, that provides an acceptable fit to the observed accelerated expansion of the Universe.Comment: 6 pages, 2 figures. Proceedings of the GGI Dark Matter and Dark Energy conferenc

TeV Dark Matter detection by Atmospheric Cerenkov Telescopes

Ground based Atmospheric Cerenkov Telescopes have recently unveiled a TeV gamma-ray signal from the direction of the Galactic Centre. We examine whether these gamma-rays, observed by the VERITAS, CANGAROO-II and HESS collaborations, may arise from annihilations of dark matter particles. Emission from nearby dwarf spheroidals, such as Sagittarius, could provide a test of this scenario.Comment: 4 pages, to appear in the proceedings of the 40th Rencontres de Moriond, "Very High Energy Phenomena in the Universe

On the exceptional specializations of big Heegner points

We extend the $p$-adic Gross-Zagier formula of Bertolini, Darmon, and Prasanna to the semistable non-crystalline setting, and combine it with our previous work to obtain a derivative formula for the specializations of Howard's big Heegner points at exceptional primes in the Hida family.Comment: 23 page

The group structure of the normalizer of Γ0(N)\Gamma_0(N)

We determine the group structure of the normalizer of $\Gamma_0(N)$ in $SL_2(\R)$ modulo $\Gamma_0(N)$. These results correct the Atkin-Lehner statement at the paper Hecke operators of $\Gamma_0(N)$

Equidistribution, L-functions, and Sato-Tate groups

In this expository note, we present an approach to the generalization of Serre of the Sato-Tate Conjecture. Most of its content is taken from Serre's original references. However, we provide a few new examples and supply references to recent progress developed in the area.Comment: 23 page

pp-adic heights of Heegner points and Beilinson-Flach elements

We give a new proof of Howard's $\Lambda$-adic Gross-Zagier formula, which we extend to the context of indefinite Shimura curves over $\mathbf{Q}$ attached to nonsplit quaternion algebras. This formula relates the cyclotomic derivative of a two-variable $p$-adic $L$-function restricted to the anticyclotomic line to the cyclotomic $p$-adic heights of Heegner points over the anticyclotomic tower, and our proof, rather than inspired by the original approaches of Gross-Zagier and Perrin-Riou, is via Iwasawa theory, based on the connection between Heegner points, Beilinson-Flach elements, and their explicit reciprocity laws.Comment: To appear in J. Lond. Math. So