arXiv subjects

Jitendra Rathore

Publications and source records attributed to Jitendra Rathore.

9 recordsLinked to original sources

arXiv2026

Unramified cohomology and Brauer--Manin pairing

We show that the Tate module of the $\ell$-adic unramified cohomology $H^3_{\nr}(X, {\Q_\ell}/{\Z_\ell})$ of a smooth projective surface $X$ over a local or strictly local field $k$ of residue characteristic prime to $\ell$ vanishes under suitable conditions. We apply this to answer some questions concerning the left and right kernels of the Brauer--Manin pairing for open subvarieties of $X$. To prove the vanishing theorem, we establish Bloch's formula for the Chow group of codimension-two cycles on a semistable model of $X$, and derive applications to the restriction map for such cycles to the closed fiber of the model.

math.AG↗

arXiv2026

Motivic Cohomology and K-groups of varieties over higher local fields

For quasi-projective varieties over a higher local field $k_N$, we prove that its $K$-groups, above a suitable degree, are divisible-by-finite. We also prove the finiteness of the prime-to-$p$ torsion subgroup of certain higher Chow groups for smooth projective varieties over such fields, where $p$ denotes the final residue characteristic of $k_N$. As an application, we show that the kernel of the tame reciprocity map is uniquely $p'$-divisible. A key ingredient in achieving these results is the finiteness of \'etale cohomology groups over such fields.

math.AG↗

arXiv2025

Zero-cycles on quasi-projective surfaces over $p$-adic fields

A conjecture of Colliot-Th\'{e}l\`{e}ne predicts that for a smooth projective variety $X$ over a finite extension $k$ of $\mathbb{Q}_p$ the kernel of the Albanese map $\text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k)$ is the direct sum of a divisible group and a finite group. In this article we show that if $\pi:X\dashrightarrow Y$ is a generically finite rational map between smooth projective surfaces and the conjecture is true for $X\otimes_k L$ for every finite extension $L/k$, then it is true for $Y$. Using work of Raskind and Spiess, this proves the conjecture for surfaces that are geometrically dominated by products of curves, under some assumptions on the reduction type of the Jacobians. The method involves studying similar questions for an open subvariety $U$ of a projective surface $X$ by replacing the Chow group of $0$-cycles with Suslin's singular homology $H_0^{\text{sus}}(U)$.

math.AG↗

arXiv2025

Torsion in abelian fundamental group and its application

We prove that the torsion subgroup of the abelian fundamental group is finite for a regular geometrically integral projective variety over a local field. We also study the structure of $SK_1(X)$ for a regular projective variety $X$ over a local field. As an application, we get class field theory for regular projective curves over local fields.

math.AG↗

arXiv2023

Duality for cohomology of split tori on curves over local fields

We prove duality theorems for the {é}tale cohomology of logarithmic Hodge-Witt sheaves and split tori on smooth curves over a local field of positive characteristic. As an application, we obtain a description of the Brauer group of the function fields of curves over local fields in terms of the characters of the idele groups. We also show that the classical Brauer-Manin pairing between the Brauer and Picard groups of smooth projective curves over local fields has analogues for arbitrary smooth curves, smooth projective curves with modulus and singular projective curves over such fields.

math.AG↗

arXiv2022

Tame class field theory over local fields

For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental group of $X$. We describe the prime-to-$p$ parts of its kernel and cokernel. This generalizes the higher dimensional unramified class field theory over local fields by Jannsen-Saito and Forre. We also prove a finiteness theorem for the geometric part of the abelian tame etale fundamental group, generalizing the results of Grothendieck and Yoshida for the unramified fundamental group.

math.AG↗

arXiv2022

A decomposition theorem for 0-cycles and applications

We prove a decomposition theorem for the cohomological Chow group of 0-cycles on the double of a quasi-projective $R_1$-scheme over a field along a closed subscheme, in terms of the Chow groups, with and without modulus, of the scheme. This yields a significant generalization of the decomposition theorem of Binda-Krishna. As applications, we prove a moving lemma for Chow groups with modulus and an analogue of Bloch's formula for 0-cycles with modulus on singular surfaces. The latter extends a previous result of Binda-Krishna-Saito.

math.AG↗

arXiv2019

Reference Setup for Quantitative Comparison of Segmentation Techniques for Short Glass Fiber CT Data

Comparing different algorithms for segmenting glass fibers in industrial computed tomography (CT) scans is difficult due to the absence of a standard reference dataset. In this work, we introduce a set of annotated scans of short-fiber reinforced polymers (SFRP) as well as synthetically created CT volume data together with the evaluation metrics. We suggest both the metrics and this data set as a reference for studying the performance of different algorithms. The real scans were acquired by a Nikon MCT225 X-ray CT system. The simulated scans were created by the use of an in-house computational model and third-party commercial software. For both types of data, corresponding ground truth annotations have been prepared, including hand annotations for the real scans and STL models for the synthetic scans. Additionally, a Hessian-based Frangi vesselness filter for fiber segmentation has been implemented and open-sourced to serve as a reference for comparisons.

cs.CV↗

arXiv2019

Fully Convolutional Deep Network Architectures for Automatic Short Glass Fiber Semantic Segmentation from CT scans

We present the first attempt to perform short glass fiber semantic segmentation from X-ray computed tomography volumetric datasets at medium (3.9 μm isotropic) and low (8.3 μm isotropic) resolution using deep learning architectures. We performed experiments on both synthetic and real CT scans and evaluated deep fully convolutional architectures with both 2D and 3D kernels. Our artificial neural networks outperform existing methods at both medium and low resolution scans.

cs.CV↗