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  1. Abstract

    Given a family of abelian covers of ${\mathbb{P}}^{1}$ and a prime $p$ of good reduction, by considering the associated Deligne–Mostow Shimura variety, we obtain non-trivial bounds for the Ekedahl–Oort types, and the Newton polygons, at prime $p$ for the curves in the family. In this paper, we investigate whether such bounds are sharp. In particular, we prove sharpness when the number of branching points is at most five and $p$ sufficiently large. Our result is a generalization under stricter assumptions of [ 2, Theorem 6.1] by Bouw, which proves the analogous statement for the $p$-rank, and it relies on the notion of Hasse–Witt triple introduced by Moonen in [ 12].

     
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  2. Abstract

    We have comprehensively studied the multiscale physical properties of the massive infrared dark cloud G28.34 (the Dragon cloud) with dust polarization and molecular line data from Planck, FCRAO-14 m, James Clerk Maxwell Telescope, and Atacama Large Millimeter/submillimeter Array. We find that the averaged magnetic fields of clumps tend to be either parallel with or perpendicular to the cloud-scale magnetic fields, while the cores in clump MM4 tend to have magnetic fields aligned with the clump fields. Implementing the relative orientation analysis (for magnetic fields, column density gradients, and local gravity), velocity gradient technique, and modified Davis–Chandrasekhar–Fermi analysis, we find that G28.34 is located in a trans-to-sub-Alfvénic environment; the magnetic field is effectively resisting gravitational collapse in large-scale diffuse gas, but is distorted by gravity within the cloud and affected by star formation activities in high-density regions, and the normalized mass-to-flux ratio tends to increase with increasing density and decreasing radius. Considering the thermal, magnetic, and turbulent supports, we find that the environmental gas of G28.34 is in a supervirial (supported) state, the infrared dark clumps may be in a near-equilibrium state, and core MM4-core4 is in a subvirial (gravity-dominant) state. In summary, we suggest that magnetic fields dominate gravity and turbulence in the cloud environment at large scales, resulting in relatively slow cloud formation and evolution processes. Within the cloud, gravity could overwhelm both magnetic fields and turbulence, allowing local dynamical star formation to happen.

     
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    Free, publicly-accessible full text available April 29, 2025