Iwasawa theory and p-adic L-functions over Zp2-extensions

We construct a two-variable analogue of Perrin-Riou’s p-adic regulator map for the Iwasawa cohomology of a crystalline representation of the absolute Galois group of Q p , over a Galois extension whose Galois group is an abelian p-adic Lie group of dimension 2. We use this regulator map to study p-adic representations of global Galois groups over certain abelian extensions of number fields whose localisation at the primes above p is an extension of the above type. In the example of the restriction to an imaginary quadratic field of the representation attached to a modular form, we formulate a conjecture on the existence of a “zeta element”, whose image under the regulator map is a p-adic L-function. We show that this conjecture implies the known properties of the 2-variable p-adic L-functions constructed by Perrin-Riou and Kim

Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and diffeomorphisms relative to which they are generalized Lie groups or topological groups. Among such topologies pairwise incomparable are found as well. Topological perfectness of the diffeomorphism group relative to certain topologies is studied. There are proved theorems about projective limit decompositions of these groups and their compactifications for compact manifolds. Moreover, an existence of one-parameter local subgroups of diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad

Critical slope p-adic L-functions of CM modular forms

For ordinary modular forms, there are two constructions of a p-adic L-function attached to the non-unit root of the Hecke polynomial, which are conjectured but not known to coincide. We prove this conjecture for modular forms of CM type, by calculating the the critical-slope L-function arising from Kato's Euler system and comparing this with results of Bellaiche on the critical-slope L-function defined using overconvergent modular symbols.Comment: 14 page

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

An environmentally induced tidal periodicity of microgrowth increment formation in subtidal populations of the clam Ruditapes philippinarum

The periodicity of increment formation in the shell of the Manila clam Ruditapes philippinarum was investigated in the subtidal zone of the Auray River estuary (South Brittany, France). Calcein markings were performed at different periods between May and October 2007 using in situ benthic chambers tented by scuba divers. This study shows that shell microgrowth increments were well-defined and deposited with a tidal periodicity in the subtidal zone, providing the calendar base for high-resolution ecological studies and environmental reconstruction from these R. philippinarum shells. Endogenous rhythmicity in shell microgrowth increment formation and oxygen consumption was previously documented in this species from intertidal flats. Our study suggests that, in the subtidal zone, Manila clams' rhythmic activity may be controlled by such an endogenous process, synchronized by tidal cues. As in other bivalves, R. philippinarum is an osmoconformer euryhaline bivalve. The tidal rhythmicity of shell microgrowth increments in subtidal specimens of this species could be explained by a behavioral adaptation of valve closure at low tide to protect the clam from low salinities and/or to synchronize with food availability. Finally, large inter-individual variability in tidally associated growth rates and asynchronous growth breaks were observed, and could be due to genetic variability between individuals, asynchronous partial spawning events or predation

Habitat usage of a groundwater-fed coastal inlet by the iconic and endangered queen conch Strombus gigas, Yucatan Peninsula, Mexico\ud

Submarine groundwater discharge from shallow karst aquifers is the dominant process delivering terrestrial water to the ocean along the Yucatan coastline. Groundwater-fed coastal inlets ('caletas') have a large diversity in aquatic environments (freshwater swamp to fully marine ecosystems) as a result of large salinity gradients. Not widely recognised, significant populations of the queen conch Strombus gigas - one of the most important fishery resources of the region - are found in these caletas. These 'un-accounted' nearshore habitats may constitute an important refuge for this species, which is most commonly reported to inhabit offshore seagrass beds. Although it is widely recognized that a good understanding of an animal’s usage of its habitat is essential to successful fisheries management, little is known on the animals' usage of the caletas, and their relation to the hydrology.\ud \ud Preliminary observations of the conch population in a groundwater-fed caleta suggest that the 'upstream' section of the caleta with greatest influence of groundwater appears to be preferentially populated by juvenile conch, whereas adults dominate the population at the mouth. An acoustic animal telemetry study, together with a hydrological monitoring program, is now underway to study the conchs' movements and their relation with the salinity gradient. Initial results indicate distinct patterns of conch movement within the caleta in relation to the hydrological gradient. Potential hydro-ecological drivers of the movement ecology of the animals, including food availability and predation in response to the groundwater-supported salinity gradient, are discussed

Variability in diel and seasonal in situ metabolism of the tropical gastropod Tectus niloticus

Researchers often use metabolic measurements in the field over narrow time periods to estimate an organism's metabolism over large time scales. Here, we measured in situ respiration, calcification and excretion rates of the tropical gastropod Tectus niloticus L. through benthic chamber experiments. Our samples spanned a 21 h time frame and were taken during both the warm and cool seasons. We assessed diel and seasonal variability in metabolic rates, as well as the effect of individual size and the contribution of shell epi-and endobionts. Our results show that metabolic rates vary through time at both diel and seasonal scales, as measured fluxes for respiration and calcification were significantly higher at night during the warm season. This nocturnal pattern was not significant in the cool season. Size effects were significant with higher respiration and calcification rates for small individuals regardless of the season, although the difference tended to be more pronounced in the warm season. We also found that shell epi-and endobionts made an important contribution to respiration, as 40 and up to 100% of total measured fluxes for night and day, respectively, could be attributed to the shell community. More importantly, the direction of the measured flux was occasionally opposite that of the individual trochus, highlighting that the contribution of shell epi-and endobionts must be accounted for in order to achieve an accurate understanding of individual metabolism. Lastly, depending on the time of day and season when measurements are taken, ignoring diel or seasonal variations in metabolic rates could result in important under-or overestimation of the contributions of gastropods to carbon and calcium carbonate fluxes in coastal ecosystems