arXiv subjects

Takeshi Tsuji

Publications and source records attributed to Takeshi Tsuji.

9 recordsLinked to original sources

arXiv2026

Twisting Higgs Modules and Functorial Aspects of the p-adic Simpson Correspondence

The classical Simpson correspondence describes complex linear representations of the fundamental group of a smooth complex projective variety in terms of linear algebra objects, namely Higgs bundles. Its p-adic analogue, introduced by G. Faltings, aims to understand continuous p-adic representations of the geometric fundamental group of a smooth projective variety over a p-adic local field. The main goal of this work is to establish a robust framework for studying the functoriality of the p-adic Simpson correspondence. We introduce a new method for twisting Higgs modules via Higgs-Tate algebras. This construction builds on one of our earlier approaches to the p-adic Simpson correspondence, which it recovers as a special case. The resulting framework yields twisted pullbacks and higher direct images of Higgs modules, thereby enabling a systematic study of the functoriality of the p-adic Simpson correspondence under arbitrary pullbacks and proper (log)smooth direct images, including for morphisms that do not admit liftings to the infinitesimal deformations used in the construction of the correspondence. We also clarify how this new twisting relates to the constructions of Heuer and Heuer-Xu, involving line bundles on the spectral variety.

math.AG↗

arXiv2025

Machine learning-based upscaling of rock permeability from pore scale to core scale: effect of training dataset size and sub-core volumes

Permeability characterizes the capacity of porous formations to conduct fluids, thereby governing the performance of carbon capture, utilization, and storage (CCUS), hydrocarbon extraction, and subsurface energy storage. A reliable assessment of rock permeability is therefore essential for these applications. Direct estimation of permeability from low-resolution CT images of large rock samples offers a rapid approach to obtain permeability data. However, the limited resolution fails to capture detailed pore-scale structural features, resulting in low prediction accuracy. To address this limitation, we propose a convolutional neural network (CNN)-based upscaling method that integrates high-precision pore-scale permeability information into core-scale, low-resolution CT images. In our workflow, the large core sample is partitioned into sub-core volumes, whose permeabilities are predicted using CNNs. The upscaled permeability at the core scale is then determined through a Darcy flow solver based on the predicted sub-core permeability map. Additionally, we examine the optimal sub-core volume size that balances computational efficiency and prediction accuracy. This framework effectively incorporates small-scale heterogeneity, enabling accurate permeability upscaling from micrometer-scale pores to centimeter-scale cores.

physics.geo-ph↗

arXiv2025

Prismatic cohomology and $A_{\inf}$-cohomology with coefficients

For a smooth $p$-adic formal scheme over the ring of integers of a perfectoid field of mixed characteristic $(0,p)$ containing all $p$-power roots of unity, we prove that the prismatic cohomology of a locally finite free prismatic crystal is isomorphic to the $A_{\inf}$-cohomology of the corresponding relative Breuil-Kisin-Fargues module, which is a certain type of locally finite free $\mathbb{A}_{\inf}$-module, on the proétale site of the generic fiber. We use a global description of the former in terms of $q$-Higgs modules via cohomological descent. We also discuss its compatibility with inverse image functors, scalar extensions under Frobenius, and tensor products.

math.AG↗

arXiv2024

Prismatic crystals and $q$-Higgs fields

Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a $q$-Higgs module and the associated $q$-Higgs complex on the bounded prismatic envelope of an embedding into a framed smooth algebra, when the base bounded prism is defined over the $q$-crystalline prism. We also discuss its behavior under the scalar extension by the Frobenius lifting and tensor products, and a global description of the cohomology of a prismatic crystal via Zariski cohomological descent.

math.AG↗

arXiv2023

Assessing the optimal contributions of renewables and carbon capture and storage toward carbon neutrality by 2050

Building on the carbon reduction targets agreed in the Paris Agreements, many nations have renewed their efforts toward achieving carbon neutrality by the year 2050. In line with this ambitious goal, nations are seeking to understand the appropriate combination of technologies which will enable the required reductions in such a way that they are appealing to investors. Around the globe, solar and wind power lead in terms of renewable energy deployment, while carbon capture and storage (CCS) is scaling up toward making a significant contribution to deep carbon cuts. Using Japan as a case study nation, this research proposes a linear optimization modeling approach to identify the potential contributions of renewables and CCS toward maximizing carbon reduction and identifying their economic merits over time. Results identify that the combination of these three technologies could enable a carbon dioxide emission reduction of between 55 and 67 percent in the energy sector by 2050 depending on resilience levels and CCS deployment regimes. Further reductions are likely to emerge with increased carbon pricing over time.

eess.SY↗

arXiv2021

Generalised representations as q-connections in integral $p$-adic Hodge theory

We relate various approaches to coefficient systems in relative integral $p$-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over $A_{\text{inf}}$ inspired by Faltings, modules with q-connection in the sense of q-de Rham cohomology, crystals on the prismatic site of Bhatt--Scholze, and q-deformations of Higgs bundles.

math.NT↗

arXiv2015

A variational formulation for dissipative fluids with interfaces in an inhomogeneous temperature field

We propose a formalization for dissipative fluids with interfaces in an inhomogeneous temperature field from the viewpoint of a variational principle. Generally, the Lagrangian of a fluid is given by the kinetic energy density minus the internal energy density. The necessary condition for minimizing an action with subject to the constraint of entropy yields the equation of motion. However, it is sometimes to know the proper equation of entropy. Our main purpose is to obtain it by using the three requirements, which are a generalization of Noether's Theorem, the second law of thermodynamics, and well-posedness. To illustrate this approach, we investigate several phenomena in an inhomogeneous temperature field. In the case of vaporization, diffusion and the rotation of a chiral liquid crystals, we clarify the cross effects between the entropy flux and these phenomena via the internal energy.

physics.flu-dyn↗

arXiv2014

A formulation for dissolution in inhomogeneous temperature field

We propose equations governing the dissolution in inhomogeneous temperature field in terms of the variational principle. The derived equations clarify that the interface energy between solute and solvent has a significant effect on the process of the dissolution. The interface energy restrains the dissolution, and the moving interface involves the heat of dissolution.

physics.flu-dyn↗

arXiv2008

On the de Rham and p-adic realizations of the Elliptic Polylogarithm for CM elliptic curves

In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then the specializations to torsion points of the p-adic elliptic polylogarithm are related to p-adic Eisenstein-Kronecker numbers, proving a p-adic analogue of the result of Beilinson and Levin expressing the complex elliptic polylogarithm in terms of Eisenstein-Kronecker-Lerch series. Our result is valid even if the elliptic curve has supersingular reduction at p.

math.NT↗