p-adic equidistribution of CM points

Let $X$ be a modular curve and consider a sequence of Galois orbits of CM points in $X$, whose $p$-conductors tend to infinity. Its equidistribution properties in $X({\bf C})$ and in the reductions of $X$ modulo primes different from $p$ are well understood. We study the equidistribution problem in the Berkovich analytification $X_{p}^{\rm an}$ of $X_{{\bf Q}_{p}}$. We partition the set of CM points of sufficiently high conductor in $X_{{\bf Q}_{p}}$ into finitely many explicit \emph{basins} $B_{V}$, indexed by the irreducible components $V$ of the mod-$p$ reduction of the canonical model of $X$. We prove that a sequence $z_{n}$ of local Galois orbits of CM points with $p$-conductor going to infinity has a limit in $X_{p}^{\rm an}$ if and only if it is eventually supported in a single basin $B_{V}$. If so, the limit is the unique point of $X_{p}^{\rm an}$ whose mod-$p$ reduction is the generic point of $V$. The result is proved in the more general setting of Shimura curves over totally real fields. The proof combines Gross's theory of quasicanonical liftings with a new formula for the intersection numbers of CM curves and vertical components in a Lubin--Tate space.Comment: Some improvements in the exposition. 23 pages, 1 new figur

The p-adic Gross-Zagier formula on Shimura curves

We prove a general formula for the $p$-adic heights of Heegner points on modular abelian varieties with potentially ordinary (good or semistable) reduction at the primes above $p$. The formula is in terms of the cyclotomic derivative of a Rankin-Selberg $p$-adic $L$-function, which we construct. It generalises previous work of Perrin-Riou, Howard, and the author, to the context of the work of Yuan-Zhang-Zhang on the archimedean Gross-Zagier formula and of Waldspurger on toric periods. We further construct analytic functions interpolating Heegner points in the anticyclotomic variables, and obtain a version of our formula for them. It is complemented, when the relevant root number is $+1$ rather than $-1$, by an anticyclotomic version of the Waldspurger formula. When combined with work of Fouquet, the anticyclotomic Gross-Zagier formula implies one divisibility in a $p$-adic Birch and Swinnerton-Dyer conjecture in anticyclotomic families. Other applications described in the text will appear separately.Comment: 75 pages. The present version is identical to the previous one (and to the published version), except for footnotes signalling that the main theorem is off by a factor of 2. A list of errata is contained in the author's "The p-adic Gross-Zagier formula on Shimura curves, II", Appendix

Zola à l’épreuve de la censure d’état et de l’Index

il saggio analizza i due tipi di censura che hanno colpito l'opera di Zola,in primo luogo, la censura di stato in Francia, in secondo luogo quella religiosa dell'Indice di Roma. Dopo aver esaminato i fatti, ho tentato di mostrare la strategia adottata da Zola per rispondervi sia nelle sue prese di posizione pubbliche sia nelle sue opere di finzione ( per esempio nel romanzo "Rome"). Viene evidenziata "la stratégie de dévoilement" di cui vengono analizzate le diverse modalità espressive: discorsive e narrative

Theta cycles

We introduce `canonical' classes in the Selmer groups of certain Galois representations with a conjugate-symplectic symmetry. They are images of special cycles in unitary Shimura varieties, and defined uniquely up to a scalar. The construction is a slight refinement of one of Y. Liu, based on the conjectural modularity of Kudla's theta series of special cycles. For 2-dimensional representations, Theta cycles are (the Selmer images of) Heegner points. In general, they conjecturally exhibit an analogous strong relation with the Beilinson--Bloch--Kato conjecture in rank 1, for which we gather the available evidence.Comment: 19 pages, comments welcom

A NONPARAMETRIC TEST OF ADVERTISING'S EFFECTIVENESS

Nonparametric demand analysis uses axioms of revealed preference to test a data set for compatibility with the hypothesis of stable preferences. Previous applications have tested for the presence of structural change using this approach. This paper shows how to include demand shifters such as advertising in the analysis. It is shown that the implied results for changes in tastes depend on restrictions on advertising's effects.Marketing,

Poème en prose et formes brèves au milieu du xixe siècle

L’auteur de l’article vise à examiner l’apport de la presse dans la définition, la pratique et le développement d’une nouvelle forme poétique en prose dans les années 1840-1860 du xixe siècle en France. Elle tend à démontrer qu’un tel renouvellement poétique ne peut être dûment analysé que si l’on opère une distinction entre les formes brèves du journal et les formes les plus longues (chroniques, contes et certains faits divers), les unes et les autres n’ayant pas toujours joué le même rôle dans l’histoire du poème en prose. Si les premières ont marqué la poésie de l’avant-garde dont les traces peuvent déjà être trouvées vers la fin du xixe siècle, dans les années qui ont succédé les décennies examinées, lors des années 1840-1860, le poème en prose se développe surtout dans le cadre des formes longues et plus légitimées auxquelles se sont essayés les écrivains majeurs du siècle. Car un tel cadre permet mieux, pour la nature et l’extension de celles-ci, d’accueillir les nouvelles compositions de la modernité et de développer les différentes formes de dualisme oxymorique qui les caractérisent.The author of this article examines the contribution of the press in defining, practising and developing a new poetic form of prose during the 1840s-60s in France. She seeks to demonstrate that this renewed poetic can be analyzed only if there is a clearly recognized distinction between the brief and the longer newspaper forms (columns, stories and certain factual exposés), given their differing roles in the history of the poem in prose. While the short form signaled the poetry of the avant-garde, traces of which were already evident at the end of the 19th century, i.e., after the 1840s-60s, the poem in prose developed largely within the framework of the longer, more legitimate forms used by major 19th century writers, since this framework was more conducive to the new modern compositions frequently characterized by forms of oxymoric dualism

IS COMMUNITY INVOLVEMENT BENEFICIAL FOR PUBLIC POLICY EFFICIENCY?

Replaced with revised version of paper 08/02.Political Economy,

On the non-vanishing of pp-adic heights on CM abelian varieties, and the arithmetic of Katz pp-adic LL-functions

Let $B$ be a simple CM abelian variety over a CM field $E$, $p$ a rational prime. Suppose that $B$ has potentially ordinary reduction above $p$ and is self-dual with root number $-1$. Under some further conditions, we prove the generic non-vanishing of (cyclotomic) $p$-adic heights on $B$ along anticyclotomic $\Z_{p}$-extensions of $E$. This provides evidence towards Schneider's conjecture on the non-vanishing of $p$-adic heights. For CM elliptic curves over \Q, the result was previously known as a consequence of work of Bertrand, Gross--Zagier and Rohrlich in the 1980s. Our proof is based on non-vanishing results for Katz $p$-adic $L$-functions and a Gross--Zagier formula relating the latter to families of rational points on $B$.Comment: Ann. Inst. Fourier, to appea