University of French Polynesia

We develop an explicit geometric construction of automorphisms of finite fields arising from isogeny cycles. Let k be a finite field, E/k an elliptic curve, and ℓ an integer coprime to char(k). Let h⊆End(E) be an ideal dividing (ℓ), and consider the corresponding torsion subgroup E[h]⊆E[ℓ]. From the action of End(E) on E[h], we construct the splitting field K of the x-coordinates of points in E[h] and the associated Galois group Gal(K/k). This yields (End(E)/h)⁎→Gal(K/k) a group homomorphism.

Understanding how environmental gradients shape species distributions is essential for managing coral reef lagoons, where habitat heterogeneity drives benthic biodiversity. This study aims to establish the ecological baseline for the pen shell Atrina vexillum in the Society Archipelago (French Polynesia) by identifying the environmental factors structuring its distribution, size variation, and habitat use. Specifically, we tested whether depth and substrate jointly influence occurrence and shell size, and whether settlement patterns deviate from habitat availability across islands. Using stratified underwater surveys, we recorded over 2600 individuals and measured shell width, depth, and substrate type. Habitat-use analyses revealed non-random settlement patterns: coral substrates were consistently under-used relative to availability, while sand and muddy-sand were more used, sometime mixed with branching corals, with significant island-specific deviations from availability (χ2 tests, p < 0.001). Shell width showed a weak positive association with depth (ρ = 0.26, p < 0.001), an effect mainly driven by Bora-Bora where a pronounced depth gradient was sampled; other islands showed limited or no detectable depth-related size differences. Although abundance varied by more than an order of magnitude among islands, size distributions were mostly unimodal, a pattern consistent with continuous recruitment, but without clear evidence of recent, distinct cohorts. These findings identify A. vexillum as a key component of soft-bottom communities when they occur in numbers whose distribution and morphology are shaped by geomorphology. Recognizing its role as a sediment-stabilizing, filter-feeding ecosystem engineer can inform lagoon zoning and conservation strategies aimed at sustaining benthic functions and resilience in Polynesian reef ecosystems.

Let E be a supersingular elliptic curve defined over 𝔽̅_p and E^(p) be its conjugate. We give a bound on the minimal degree of an isogeny from E to E^(p) depending on p, and show that this bound is both asymptotically optimal as well as sharp in many cases. This bound is obtained by developing a new technique to compute the degree of certain isogenies from a supersingular elliptic curve to its conjugate, and we present extensive computations of the successive minima of the lattice containing these isogenies. Following this, we give several conjectures supported by the data we have obtained, including some on the set of primes p for which the bound we give in this article is attained.

Study region The Island of Tahiti, prone to heavy rainfall and flash floods that regularly cause severe damage. Study focus The aim of this paper is to build a rainfall-runoff model to estimate floods in any catchment of the island. A distributed conceptual and parsimonious event-based model was designed to fit the observed hydrological spatial variability. It combines the SCS-SMA (Soil Conservation Service - Soil Moisture Accounting) as a runoff production function with a Lag-and-Route routing function, both operating over a mesh of cells. The complete model was calibrated in 11 catchments across the island, and their parameters were related to catchment descriptors related to soil moisture, geology and level of urbanization. New Hydrological Insights for the Region Two parameters were chosen to handle the hydrological variability between catchments: the initial level in the reservoir of the runoff model, H0, and an index linked to the flow velocity in the routing model, µ. For natural catchments, an effective relationship was established between the median values of H0 and the index of regionalized antecedent precipitation. The proportion of urbanization was a secondary factor in explaining H0. µ was related to the geological characteristics of the catchment. This rainfall-runoff model can be used to calculate design floods for the whole island of Tahiti, but needs to be improved for use in flood forecasting for real events.

Marine heatwaves (MHWs) are increasingly studied in climate sciences for their ecological impacts, for which accurate real-time bulletins and forecasts are essential. Yet, methodological choices in their detection affect metric estimates, underlining the need to better assess these sensitivities. This study provides a thorough assessment of the impact of sea surface temperature (SST) product choice on MHW statistics, focusing on the tropical Pacific. MHW detection was performed on six daily gridded SST datasets: four widely used blended satellite observational products, one ocean reanalysis, and a multi-dataset ensemble mean computed from the four observational products. Sensitivity to SST products was evaluated for six MHW metrics (MHW days per year, number of events per year, duration, maximum intensity, cumulative intensity and onset rate) and for the degree heating weeks (DHW), a widely used index for coral bleaching risk. Inter-product comparisons revealed a significant dispersion among MHW metric estimates. The reanalysis GLORYS12v1 detected fewer, longer and less intense MHWs while OISST detected more MHWs of shorter duration and higher intensity. likely related to the respectively weak and strong high-frequency SST variability (periods shorter than 2 weeks) of the two products. The sensitivity analysis showed that the onset rate was the most sensitive metric to SST product choice and the maximum intensity the most robust one. Metrics uncertainties were quantified inside seven regions of the basin and were largest in the western Pacific Warm Pool. Co-occurrence analyses of MHWs revealed that, over the basin, 10 % to 80 % of MHW days were detected simultaneously by all products, with the western Pacific Warm Pool showing the lowest agreement (10 %–40 %). Filtering MHWs by size also revealed that the detection of large-scale MHWs (>5°lon×5°lat) was more consistent across products than smaller-scale ones. Finally, over the studied period, inter-product differences tended to decrease with time. The DHW also revealed to be sensitive to SST products, with inter-product differences on DHW annual maximum reaching more than 1 °C weeks and percentages of bleaching alert days (DHW≥4 °C weeks) in common across products reaching 70 % at most across much of the basin. These findings contribute to a better understanding of how SST product choice affects the characterization of MHWs and DHW, and their associated uncertainties.