Past and future plant diversity of a coastal wetland driven by soil subsidence and climate change

On the island of Ameland (The Netherlands), natural gas has been extracted from a dune and salt marsh natural area since 1986. This has caused a soil subsidence of c. 1–25 cm, which can be used as a model to infer effects of future sea level rise. The aims of our study were (a) to relate the changes in the vegetation, and more specifically, in plant diversity, during the extraction period to soil subsidence and weather fluctuations, and (b) to use these relations to predict future changes due to the combination of ongoing soil subsidence and climate change. We characterised climate change as increases in mean sea level, storm frequency and net precipitation. Simultaneous observations were made of vegetation composition, elevation, soil chemistry, net precipitation, groundwater level, and flooding frequency over the period 1986–2001. By using multiple regression the changes in the vegetation could be decomposed into (1) an oscillatory component due to fluctuations in net precipitation, (2) an oscillatory component due to incidental flooding, (3) a monotonous component due to soil subsidence, and (4) a monotonous component not related to any measured variable but probably due to eutrophication. The changes were generally small during the observation period, but the regression model predicts large changes by the year 2100 that are almost exclusively due to sea level rise. However, although sea level rise is expected to cause a loss of species, this does not necessarily lead to a loss of conservancy valu

Tensor Products of Convex Cones, Part II: Closed Cones in Finite-Dimensional Spaces

In part I, we studied tensor products of convex cones in dual pairs of real vector spaces. This paper complements the results of the previous paper with an overview of the most important additional properties in the finite-dimensional case. (i) We show that the projective cone can be identified with the cone of positive linear operators that factor through a simplex cone. (ii) We prove that the projective tensor product of two closed convex cones is once again closed (Tam already proved this for proper cones). (iii) We study the tensor product of a cone with its dual, leading to another proof (and slight extension) of a theorem of Barker and Loewy. (iv) We provide a large class of examples where the projective and injective cones differ. As this paper was being written, this last result was superseded by a result of Aubrun, Lami, Palazuelos and Pl\'avala, who independently showed that the projective cone $E_+ \mathbin{\otimes_\pi} F_+$ is strictly contained in the injective cone $E_+ \mathbin{\otimes_\varepsilon} F_+$ whenever $E_+$ and $F_+$ are closed, proper and generating, with neither $E_+$ nor $F_+$ a simplex cone. Compared to their result, this paper only proves a few special cases.Comment: 21 page

The equivalence of several conjectures on independence of ℓ\ell

We consider several conjectures on the independence of $\ell$ of the \'etale cohomology of (singular, open) varieties over $\bar{\mathbf F}_p$. The main result is that independence of $\ell$ of the Betti numbers $h^i_{\text{c}}(X,\mathbf Q_\ell)$ for arbitrary varieties is equivalent to independence of $\ell$ of homological equivalence $\sim_{\text{hom},\ell}$ for cycles on smooth projective varieties. We give several other equivalent statements. As a surprising consequence, we prove that independence of $\ell$ of Betti numbers for smooth quasi-projective varieties implies the same result for arbitrary separated finite type $k$-schemes.Comment: 25 pages. Fixed typos and other minor correction

Dominating varieties by liftable ones

Algebraic geometry in positive characteristic has a quite different flavour than in characteristic zero. Many of the pathologies disappear when a variety admits a lift to characteristic zero. It is known since the sixties that such a lift does not always exist. However, for applications it is sometimes enough to lift a variety dominating the given variety, and it is natural to ask when this is possible. The main result of this dissertation is the construction of a smooth projective variety over any algebraically closed field of positive characteristic that cannot be dominated by another smooth projective variety admitting a lift to characteristic zero. We also discuss some cases in which a dominating liftable variety does exist