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Yufan Luo

Publications and source records attributed to Yufan Luo.

12 recordsLinked to original sources
arXiv2026

On the bounded-conductor finiteness conjecture in equal characteristic

We investigate the equal-characteristic case of the Moon--Taguchi bounded-conductor finiteness conjecture for mod $p$ Galois representations over global function fields. We first establish a conditional finiteness theorem: for any global function field $K$ of characteristic $p$ and any integer $n \ge 1$, there are only finitely many isomorphism classes of continuous, semisimple, everywhere unramified, and geometric representations $\rho: G_K \to \mathrm{GL}_n(\overline{\mathbf{F}}_p)$ that admit an everywhere unramified characteristic-zero lift. Furthermore, we prove that the conjecture fails in general without this lifting hypothesis. Concretely, we construct infinitely many global function fields $K$ of characteristic $p$ admitting a continuous, surjective, absolutely irreducible, everywhere unramified, and geometric representation $\rho_r: G_K \twoheadrightarrow \mathrm{SL}_2(\mathbf{F}_{p^r})$ for each integer $r \ge 4$. As a corollary, we construct an everywhere unramified Galois extension \(L/K\), regular over \(\mathbf F_p\), with Galois group \[ \mathrm{Gal}(L/K)\cong \prod_{r\geq4}\mathrm{PSL}_2(\mathbf F_{p^r}). \] Combined with known cross-characteristic finiteness theorems, this completely resolves the question posed by Moon and Taguchi in dimension two: such extensions exist over global function fields of characteristic \(p\), whereas they cannot exist over global function fields of characteristic different from \(p\).

math.NT↗
arXiv2026

On the Finiteness of Geometric Representations for Varieties over Finite Fields

Let $p$ be a prime number, and let $k$ be a finite field of characteristic different from $p$. Let $X$ be a normal geometrically connected variety over $k$, let $\overline X$ be a compactification of $X$, and let $Z=\overline X\setminus X$. Let $D$ be an effective Cartier divisor on $\overline X$ whose support is contained in $Z$. Motivated by Hiranouchi's Hermite--Minkowski type theorem for varieties over finite fields, we formulate a finiteness conjecture for continuous semisimple geometric representations $$ \pi_1(X,D)\longrightarrow \operatorname{GL}_n(F), $$ where $\pi_1(X,D)$ is Hiranouchi's fundamental group with ramification bounded by $D$, and $F$ is an algebraically closed field of characteristic $p$ endowed with the discrete topology. We prove this conjecture for odd $p$ in the following two cases: for curves with arbitrary ramification bound $D$, and for varieties of arbitrary dimension in the tame case, namely $D=0$. Furthermore, for arbitrary $p$, we prove the finiteness for those representations which admit a lift to characteristic zero.

math.NT↗
arXiv2026

A finiteness theorem for mod $p$ Galois representations over global function fields

Let $p$ be an odd prime number and let $\overline{\mathbb{F}}_p$ be a fixed algebraic closure of the finite field of order $p$. Let $K$ be a global function field of characteristic different from $p$ and let $G_{K}$ be the absolute Galois group of $K$. We prove that there are only finitely many isomorphism classes of continuous geometric semisimple representations $\rho:G_{K}\to \mathrm{GL}_{n}(\overline{\mathbb{F}}_{p})$ such that their Artin conductors are bounded. It is worth emphasizing that we do not need to assume that $p$ does not divide $n$.

math.NT↗
arXiv2026

Remarks on the Boston Unramified Fontaine-Mazur Conjecture, II

In this paper, we investigate Boston's generalization of the unramified Fontaine-Mazur conjecture for Galois representations. From a group-theoretic perspective, we first show that the conjecture can be reduced to the case of certain distinguished classes of $p$-adic analytic groups and $\mathbb{F}_{p}[[T]]$-adic analytic groups. Specifically, these are open subgroups of the groups of integral points of absolutely simple algebraic groups defined over non-Archimedean local fields. Furthermore, we provide a group-theoretic interpretation of the conjecture in terms of the virtually Golod-Shafarevich property. Finally, we establish a local-global principle and a prime-to-adjoint principle for the conjecture.

math.NT↗
arXiv2026

Dean's conjecture and cycles modulo k

Dean conjectured three decades ago that every graph with minimum degree at least $k\ge 3$ contains a cycle whose length is divisible by $k$. While the conjecture has been verified for $k\in \{3,4\}$, it remains open for $k\ge 5$. A weaker version, also proposed by Dean, asserting that every $k$-connected graph contains a cycle of length divisible by $k$, was resolved by Gao, Huo, Liu, and Ma using the notion of admissible cycles. In this paper, we resolve Dean's conjecture for all $k\ge 6$. In fact, we prove a stronger result by showing that every graph with minimum degree at least $k$ contains cycles of length $r \pmod k$ for every even integer $r$, unless every end-block belongs to a specific family of exceptional graphs, which fail only to contain cycles of length $2 \pmod k$. We also establish a strengthened result on the existence of admissible cycles. Our proof introduces two sparse graph families, called trigonal graphs and tetragonal graphs, which provide a flexible framework for studying path and cycle lengths and may be of independent interest.

math.CO↗
arXiv2025

On the second partial Global Euler-Poincare characteristics for Galois cohomology

Let $K$ be a number field, let $S$ be a finite set of primes of $K$ containing all archimedean primes, and let $G_{K,S}$ denote the Galois group of the maximal extension of $K$ unramified outside $S$. In this paper, we study the second partial Euler--Poincar\'e characteristic $\chi_{2}(G_{K,S},M)$ for a finite $G_{K,S}$-module $M$, without imposing the condition that the order of $M$ is an $S$-unit. By adjoining a further finite set of primes of $K$, which can be chosen to be disjoint from any prescribed set of primes of density zero, we obtain an explicit formula for the corresponding second partial Euler--Poincar\'e characteristic. As an application, we investigate the presentation of the Galois group $G_{K,S}$. Furthermore, for any number field, we construct counterexamples to the dimension conjecture for Galois deformation rings.

math.NT↗
arXiv2024

On the Boston's Unramified Fontaine-Mazur Conjecture

This paper studies the Unramified Fontaine-Mazur Conjecture for $ p $-adic Galois representations and its generalizations. We prove some basic cases of the conjecture and provide some useful criterions for verifying it. In addition, we propose several different strategies to attack the conjecture and reduce it to some special cases. We also prove many new results of the conjecture in the two-dimensional case. Furthermore, we also study the unramified Galois deformation rings. Assuming the Unramified Fontaine-Mazur conjecture, we prove that the generic fiber of the unramified deformation ring is a finite direct product of fields. In particular, the unramified deformation ring has only finitely many $\overline{\mathbb{Q}}_{p}$-valued points. We also give some counterexamples to the so-called dimension conjecture for Galois deformation rings assuming the conjecture.

math.NT↗
arXiv2021

DeepACC:Automate Chromosome Classification based on Metaphase Images using Deep Learning Framework Fused with Prior Knowledge

Chromosome classification is an important but difficult and tedious task in karyotyping. Previous methods only classify manually segmented single chromosome, which is far from clinical practice. In this work, we propose a detection based method, DeepACC, to locate and fine classify chromosomes simultaneously based on the whole metaphase image. We firstly introduce the Additive Angular Margin Loss to enhance the discriminative power of model. To alleviate batch effects, we transform decision boundary of each class case-by-case through a siamese network which make full use of prior knowledges that chromosomes usually appear in pairs. Furthermore, we take the clinically seven group criterion as a prior knowledge and design an additional Group Inner-Adjacency Loss to further reduce inter-class similarities. 3390 metaphase images from clinical laboratory are collected and labelled to evaluate the performance. Results show that the new design brings encouraging performance gains comparing to the state-of-the-art baselines.

cs.CV↗
arXiv2020

G-RCN: Optimizing the Gap between Classification and Localization Tasks for Object Detection

Multi-task learning is widely used in computer vision. Currently, object detection models utilize shared feature map to complete classification and localization tasks simultaneously. By comparing the performance between the original Faster R-CNN and that with partially separated feature maps, we show that: (1) Sharing high-level features for the classification and localization tasks is sub-optimal; (2) Large stride is beneficial for classification but harmful for localization; (3) Global context information could improve the performance of classification. Based on these findings, we proposed a paradigm called Gap-optimized region based convolutional network (G-RCN), which aims to separating these two tasks and optimizing the gap between them. The paradigm was firstly applied to correct the current ResNet protocol by simply reducing the stride and moving the Conv5 block from the head to the feature extraction network, which brings 3.6 improvement of AP70 on the PASCAL VOC dataset and 1.5 improvement of AP on the COCO dataset for ResNet50. Next, the new method is applied on the Faster R-CNN with backbone of VGG16,ResNet50 and ResNet101, which brings above 2.0 improvement of AP70 on the PASCAL VOC dataset and above 1.9 improvement of AP on the COCO dataset. Noticeably, the implementation of G-RCN only involves a few structural modifications, with no extra module added.

cs.CV↗
arXiv2020

DeepACEv2: Automated Chromosome Enumeration in Metaphase Cell Images Using Deep Convolutional Neural Networks

Chromosome enumeration is an essential but tedious procedure in karyotyping analysis. To automate the enumeration process, we develop a chromosome enumeration framework, DeepACEv2, based on the region based object detection scheme. The framework is developed following three steps. Firstly, we take the classical ResNet-101 as the backbone and attach the Feature Pyramid Network (FPN) to the backbone. The FPN takes full advantage of the multiple level features, and we only output the level of feature map that most of the chromosomes are assigned to. Secondly, we enhance the region proposal network's ability by adding a newly proposed Hard Negative Anchors Sampling to extract unapparent but essential information about highly confusing partial chromosomes. Next, to alleviate serious occlusion problems, besides the traditional detection branch, we novelly introduce an isolated Template Module branch to extract unique embeddings of each proposal by utilizing the chromosome's geometric information. The embeddings are further incorporated into the No Maximum Suppression (NMS) procedure to improve the detection of overlapping chromosomes. Finally, we design a Truncated Normalized Repulsion Loss and add it to the loss function to avoid inaccurate localization caused by occlusion. In the newly collected 1375 metaphase images that came from a clinical laboratory, a series of ablation studies validate the effectiveness of each proposed module. Combining them, the proposed DeepACEv2 outperforms all the previous methods, yielding the Whole Correct Ratio(WCR)(%) with respect to images as 71.39, and the Average Error Ratio(AER)(%) with respect to chromosomes as about 1.17.

cs.CV↗
arXiv2020

PBRnet: Pyramidal Bounding Box Refinement to Improve Object Localization Accuracy

Many recently developed object detectors focused on coarse-to-fine framework which contains several stages that classify and regress proposals from coarse-grain to fine-grain, and obtains more accurate detection gradually. Multi-resolution models such as Feature Pyramid Network(FPN) integrate information of different levels of resolution and effectively improve the performance. Previous researches also have revealed that localization can be further improved by: 1) using fine-grained information which is more translational variant; 2) refining local areas which is more focused on local boundary information. Based on these principles, we designed a novel boundary refinement architecture to improve localization accuracy by combining coarse-to-fine framework with feature pyramid structure, named as Pyramidal Bounding Box Refinement network(PBRnet), which parameterizes gradually focused boundary areas of objects and leverages lower-level feature maps to extract finer local information when refining the predicted bounding boxes. Extensive experiments are performed on the MS-COCO dataset. The PBRnet brings a significant performance gains by roughly 3 point of $mAP$ when added to FPN or Libra R-CNN. Moreover, by treating Cascade R-CNN as a coarse-to-fine detector and replacing its localization branch by the regressor of PBRnet, it leads an extra performance improvement by 1.5 $mAP$, yielding a total performance boosting by as high as 5 point of $mAP$.

cs.CV↗