Twisting commutative algebraic groups

If $V$ is a commutative algebraic group over a field $k$, $O$ is a commutative ring that acts on $V$, and $I$ is a finitely generated free $O$-module with a right action of the absolute Galois group of $k$, then there is a commutative algebraic group $I \otimes_O V$ over $k$, which is a twist of a power of $V$. These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori over finite fields) and to the arithmetic of abelian varieties over number fields. For purposes of such applications we devote this article to making explicit this tensor product construction and its basic properties.Comment: To appear in Journal of Algebra. Minor changes from original versio

Optical radar backscattering from the mesopause region during July and August 1967

Optical radar measurement of backscattering from mesopause region during July and August 196

On elliptic curves with an isogeny of degree 7

We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\mathbf{Q}(\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the exceptions are exactly the curves with complex multiplication. As a by-product of one of the key steps in our proof, we determine exactly when there exist elliptic curves over an arbitrary field $k$ of characteristic not 7 with a $k$-rational isogeny of degree 7 and a specified Galois action on the kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in Version 1. Version 3 will appear in the American Journal of Mathematic

Patterns and processes of soil carbon dynamics in a northeastern United States forest

Forest soils represent a substantial component of the terrestrial carbon cycle and are an important research area for a number of carbon cycle science initiatives. Whereas patterns of aboveground productivity have been relatively well measured and are increasingly included in regional-scale model analyses, belowground estimates are still highly uncertain and progress has been hampered by methodological difficulties. The lack of data poses a problem because belowground measurements are needed to create complete carbon budgets for terrestrial ecosystems at local, regional and global scales. Ecosystem carbon balances will help identify how and where carbon is being stored, as well as how carbon storage may change as forests recover from past disturbance or transition into different forest types as a result of climate changes. In this study, I examined patterns of soil respiration and belowground carbon allocation at the Bartlett Experimental Forest, a north temperate forest landscape located in New Hampshire, USA. (Abstract shortened by UMI.)

First Observations of Benthos and Seston from a Submersible in the Lower St. Lawrence Estuary

Six dives with the submersible PISCES IV have permitted a unique description of the benthic and pelagic environments of a large, deep Canadian estuary. The estuarine floor and continental slopes are divided into five depth-dependent benthic zones. In order of decreasing depth are the Bathyal Trough Zone, the lnfaunal Zone, the Ophiura Zone, the Ice Rafting Zone and the Wave Base Zone. The zonal boundaries are based on changes in the faunal community, sediment texture, current energy, level of bioturbation and suspended particulate loading. Biological resuspension appears important in the Bathyal Trough and lnfaunal Zones. Current resuspension dominates the Ophiura and Ice Rafting Zones with storm waves additionally reworking the Wave-Base sediments. Seston characteristics are strongly influenced by the source and dynamics of the host water mass. The Surface Layer, the entrained outflow from the St. Lawrence River, is the source of most suspended matter found beneath. Large particles, mostly organo-mineral aggregates, become even larger with depth and indicate a rapid downward transfer of suspended sediment. The upper Intermediate Layer is complicated by stratified zones of turbulence that temporarily reduce the floe size. With the absence of such fine water structure, the lower Intermediate Layer is characterized by long chains of marine "snow" joined by delicate filaments. The Bottom Layer, a zone of increased turbulence, had aggregates breaking up into a haze of fine particles.Six plongées à bord du submersible Pisces IV ont permis de décrire les milieux benthique et pélagique de l'estuaire, large et profond, du Saint-Laurent. Le fond de l'estuaire et les talus continentaux ont été divisés, selon la profondeur, en cinq zones benthiques. Ce sont, du fond vers la surface, la zone bathyale du chenal Laurentien, la zone endobenthique, la zone à Ophiura, la zone de dépôts glaciels et la zone sous l'influence des vagues. Ces zones ont été déterminées à partir des variations des populations macrobenthiques, de la texture des sédiments, de l'énergie des courants, du niveau de bioturbation et de la concentration des particules en suspension. La resuspension biologique semble être importante dans les zones bathyale et endobenthique, mais la resuspension par les courants domine dans les trois autres zones. Les sédiments de la zone sous l'influence des vagues peuvent aussi être remaniés par les vagues de tempêtes. Les caractéristiques du seston sont fortement influencées par la source et la dynamique des différentes masses d'eau. Une grande partie du matériel en suspension provient de la couche superficielle, entraîné par le courant du Saint-Laurent. Les grosses particules, surtout les agrégats organo-minéraux, sont de plus en plus grosses en profondeur, ce qui suppose une descente rapide du matériel en suspension vers le fond. Dans la couche intermédiaire supérieure, des zones de turbulence stratifiées réduisent temporairement la taille des agrégats. La partie inférieure de la couche intermédiaire ne contient pas de ces stratifications fines et est plutôt caractérisée par la présence de longues chaînes de particules rattachées par un filament délicat. Dans la couche de fond, l'accroissement de la turbulence transforme les agrégats en un brouillard de fines particules.Sechs Tauchmanôver mit dem U-Boot Pisces IV haben eine einzigartige Beschreibung der benthis-chen und pelagischen Umgebung einer grossen, tiefen, kanadischen Mùndung erlaubt. Der Aestuarboden und die Kon-tinentalhànge sind in fùnf tiefenbedingte benthische Zonen eingeteilt. Der Ordnung nach, in abnehmender Tiefe, liegen die bathyal Zone des Skt-Lorenz Kanals, die endobenthische Zone, die Ophiura Zone, die Eisstrandungs Zone und die Wellen-Einfluss-Zone. Die Zonengrenzen sind auf Verànderungen in der Faunenwelt, Sedimenttextur, Strômungsenergie, Niveau der Bioturbation und der Konzentration der Schwebstoffe gegrùndet. Biologische Resuspension ist in der bathyalen und endobentischen Zone wichtig, wàhrend die Resuspension durch die Strômung in der Ophiura und Eisstrandungszone ùberwiegt, mit zusàtzlicher Bearbeitung der Wellen-Basis-Elemente durch Sturmwellen. Seston Kennzeichen sind durch die Dynamik der Gastgewàsser stark beeinflusst. Ein grosser Teil der Schwebstoffe kommt aus der oberen Schicht und wird durch die Strômung des Skt Lorenz Stromes mitgeschleppt. Grosse Teile, meistens organischmineral Aggregate werden mit wachsender Tiefe noch grosser und zeigen ein schnelles Sinken der Schwebstoffe an. In der oberen Zwischenschicht verringern die stratifizierten Turbulen Zonen zeitweilig die Grosse der Aggregate. Der untere Teil der Zwischenschicht zeigt keine solche feinen Stratifikationen und kennzeichnet sich eher durch die Gegenwart von langen Ketten von Schwebstoffteilchen, die durch einen dùnnen Faden zusammenhalten. In der Grundschicht, einer Zone mit vermehrterTurbulenz, werden die Aggregate zu einem Nebel feiner Teilchen aufgebrochen