Kohei Aoyama | Searcharxiv

arXiv2026

Genus formulas for dormant modular curves and asymptotic behavior of their function fields

Towers of algebraic function fields over finite fields play a fundamental role in arithmetic geometry and coding theory. Classical examples arising from modular and Drinfeld modular curves exhibit asymptotically good behavior. In this paper, we introduce an analogous construction derived from the moduli spaces of higher-level dormant $\mathrm{PGL}_2$-opers of prescribed radii on $4$-pointed stable curves of genus $0$. These spaces, which we refer to as dormant modular curves, form projective systems under level reduction. Building on previous results in the moduli theory of dormant opers, we establish an explicit formula for computing the genera of these curves. This formula allows us to study the asymptotic behavior of the corresponding towers of function fields and to compare them with the classical modular and Drinfeld modular cases.

math.AG↗

arXiv2021

Environmental dependence of gas properties in a protocluster at z~2.5

In a protocluster USS1558-003 at z=2.53, galaxies in the dense cores show systematically elevated star-forming activities than those in less dense regions. To understand its origin, we look into the gas properties of the galaxies in the dense cores by conducting deep 1.1mm observations with Atacama Large Millimeter/submillimeter Array (ALMA). We detect interstellar dust continuum emissions from 12 member galaxies and estimate their molecular gas masses. Comparing these gas masses with our previous measurements from CO(3-2) line, we infer that the latter might be overestimated. We find that the gas to stellar mass ratios of the galaxies in the dense cores tend to be higher (at M* ~ 10^{10} M_sun) where we see the enhanced star-forming activities), suggesting that such large gas masses can sustain their high star-forming activities. However, if we compare the gas properties of these protocluster galaxies with the gas scaling relations constructed for field galaxies at similar cosmic epoch, we find no significant environmental difference at the same stellar mass and star formation rate. Although both gas mass ratios and star-forming activities are enhanced in the majority of member galaxies, they appear to follow the same scaling relation as field galaxies. Our results are consistent with the scenario that the cold gas is efficiently supplied to protocluster cores and to galaxies therein along surrounding filamentary structures, which leads to the high gas mass fractions and thus the elevated star-formation activities, but without changing the star formation law.

astro-ph.GA↗