Upper bounds for regularized determinants

Let $E$ be a holomorphic vector bundle on a compact K\"ahler manifold $X$. If we fix a metric $h$ on $E$, we get a Laplace operator $\Delta$ acting upon smooth sections of $E$ over $X$. Using the zeta function of $\Delta$, one defines its regularized determinant $det'(\Delta)$. We conjectured elsewhere that, when $h$ varies, this determinant $det'(\Delta)$ remains bounded from above. In this paper we prove this in two special cases. The first case is when $X$ is a Riemann surface, $E$ is a line bundle and $dim(H^0 (X,E)) + dim(H^1 (X,E)) \leq 2$, and the second case is when $X$ is the projective line, $E$ is a line bundle, and all metrics under consideration are invariant under rotation around a fixed axis.Comment: 22 pages, plain Te

On the arithmetic Chern character

We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern character class of the sequence and its Chern character with supports on the finite fibers. Next, we compute these classes in the situation encountered by the second author when proving a "Kodaira vanishing theorem" for arithmetic surfaces

Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties

The deformation complex is a homotopy invariant of a homotopy algebra

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an explicit construction.Comment: A revised version. The final version will appear in the volume "Current Developments and Retrospectives in Lie Theory

Do negative random shocks affect trust and trustworthiness?

We report data from a variation of the trust game aimed at determining whether (and how) inequality and random shocks that affect wealth influence the levels of trust and trustworthiness. To tease apart the effect of the shock and the inequality, we compare behavior in a trust game where the inequality is initially given and one where it is the result of a random shock that reduces the second mover’s endowment. We find that first-movers send less to second-movers but only when the inequality results from a random shock. As for the amount returned, second-movers return less when they are endowed less than first-movers, regardless of whether the difference in endowments was initially given or occurred after a random shock

Trust and trustworthiness after negative random shocks

We experimentally investigate the effect of a negative endowment shock that can cause inequality in a trust game. Our goal is to assess whether different causes of inequality have different effects on trust and trustworthiness. In our trust game, we vary whether there is inequality (in favor of the second mover) or not and whether the inequality results from a random negative shock (i.e., the outcome of a die roll) or exists from the outset. Our findings suggest that inequality causes first-movers to send more of their endowment and second-movers to return more. However, we do not find support for the hypothesis that the cause of the inequality matters. Behavior after the occurrence of a random shock is not significantly different from the behavior in treatments where the inequality exists from the outset. Our results highlight the need to be cautious when interpreting the effects on trust and trustworthiness of negative random shocks in the field (such as natural disasters). Our results suggest that these effects are primarily driven by the inequality caused by the shock and not by any of the additional characteristics of the shock, like saliency or uncertainty

Melting and Pressure-Induced Amorphization of Quartz

It has recently been shown that amorphization and melting of ice were intimately linked. In this letter, we infer from molecular dynamics simulations on the SiO2 system that the extension of the quartz melting line in the metastable pressure-temperature domain is the pressure-induced amorphization line. It seems therefore likely that melting is the physical phenomenon responsible for pressure induced amorphization. Moreover, we show that the structure of a "pressure glass" is similar to that of a very rapidly (1e+13 to 1e+14 kelvins per second) quenched thermal glass.Comment: 9 pages, 4 figures, LaTeX2

There is no degree map for 0-cycles on Artin stacks

We show that there is no way to define degrees of 0-cycles on Artin stacks with proper good moduli spaces so that (i) the degree of an ordinary point is non-zero, and (ii) degrees are compatible with closed immersions.Comment: 3 page