arXiv subjects

Ruida Di

Publications and source records attributed to Ruida Di.

4 recordsLinked to original sources

arXiv2026

Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces

Let $E$ be an $n$-dimensional rigid adelic space over a number field $K$. We study the minimum number $g_E(R)$ of proper $K$-subspaces needed to cover the projective height ball of radius $R$, together with the maximum cardinality $h_E(R)$ of a subset in linear general position. We show that, once $R$ is sufficiently large compared with the last Roy--Thunder minimum of $E$, both quantities have order $\Psi_E(R)^{[K:\mathbb Q]}$, where $\Psi_E(R)$ is an explicit expression in the Roy--Thunder minima. The comparison constants are effectively computable and uniform in $E$. For the standard adelic space $K^n$, this gives order $R^{[K:\mathbb Q]n/(n-1)}$.

math.NT↗

arXiv2026

Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces

For every $1\le d<n$, we prove joint equidistribution, as the height tends to infinity, of $d$-dimensional $K$-subspaces in a rigid adelic space over a number field $K$, together with their archimedean Grassmannian images and the $K$-linear isometry classes of the normalized subspace and quotient. We identify the leading constant, prove no escape of mass from either normalized factor, and obtain global equidistribution against bounded continuous test functions. Over a general number field, the two normalized shapes are coupled by a determinant-class relation; conditional on the determinant class, their limiting law is the product of the Haar-induced probability measures on the corresponding fibers.

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arXiv2025

A necessary condition for liftings of positive characteristic varieties with finite fundamental groups

In this paper, we introduce a necessary condition for the existence of characteristic zero liftings of certain smooth, proper varieties in positive characteristic, using etale homotopy theory and Wall's finiteness obstruction. For a variety with finite etale fundamental group pi, we define a notion of mod-l finite dominatedness based on the F_l-chain complex of the universal cover of its l-profinite etale homotopy type. We prove that such a variety X can be lifted to characteristic zero only if the above chain complex of X is quasi-isomorphic to a bounded complex of finitely generated projective F_l[pi]-modules. To prove this result, we extend Wall's discussions of finiteness obstructions to l-profinite complete spaces with finite fundamental group.

math.AT↗

arXiv2023

Uniform Bogomolov Conjecture for Tori

In this paper, we present a novel proof of the uniform Bogomolov conjecture for algebraic tori. To do this, we introduce a definition of non-degenerate subvarieties applicable to a family of algebraic tori and establish an equidistribution theorem in this setting. Our method stems from recent advancements in the uniform Mordell-Lang conjecture, particularly the breakthrough results by Dimitrov, Gao, and Habegger, as well as independent work by K\"uhne and the collaborative effort of Gao, Ge, and K\"uhne.

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