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Research Paper#p-adic Geometry, Etale Cohomology, Poincaré Duality🔬 ResearchAnalyzed: Jan 3, 2026 06:34

Mod p Poincaré Duality in p-adic Geometry

Published:Dec 31, 2025 18:29
1 min read
ArXiv

Analysis

This paper introduces a new class of rigid analytic varieties over a p-adic field that exhibit Poincaré duality for étale cohomology with mod p coefficients. The significance lies in extending Poincaré duality results to a broader class of varieties, including almost proper varieties and p-adic period domains. This has implications for understanding the étale cohomology of these objects, particularly p-adic period domains, and provides a generalization of existing computations.
Reference

“The paper shows that almost proper varieties, as well as p-adic (weakly admissible) period domains in the sense of Rappoport-Zink belong to this class.”

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Mathematics#Representation Theory, p-adic Hodge Theory🔬 ResearchAnalyzed: Jan 3, 2026 16:45

Extension Groups of Generalized Steinberg Representations

Published:Dec 30, 2025 15:07
1 min read
ArXiv

Analysis

This paper investigates extension groups between locally analytic generalized Steinberg representations of GL_n(K), motivated by previous work on automorphic L-invariants. The results have applications in understanding filtered (φ,N)-modules and defining higher L-invariants for GL_n(K), potentially connecting them to Fontaine-Mazur L-invariants.
Reference

“The paper proves that a certain universal successive extension of filtered (φ,N)-modules can be realized as the space of homomorphisms from a suitable shift of the dual of locally K-analytic Steinberg representation into the de Rham complex of the Drinfeld upper-half space.”

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Research Paper#Machine Learning, p-adic Numbers, Representation Learning🔬 ResearchAnalyzed: Jan 3, 2026 19:44

Learning with p-adic Numbers: A Novel Approach to Machine Learning

Published:Dec 27, 2025 19:40
1 min read
ArXiv

Analysis

This paper explores the use of p-adic numbers, a non-Archimedean field, as an alternative to real numbers in machine learning. It challenges the conventional reliance on real-valued representations and Euclidean geometry, proposing a framework based on the hierarchical structure of p-adic numbers. The work is significant because it opens up a new avenue for representation learning, potentially offering advantages in areas like code theory and hierarchical data modeling. The paper's theoretical exploration and the demonstration of representing semantic networks highlight its potential impact.
Reference

“The paper establishes the building blocks for classification, regression, and representation learning with the $p$-adics, providing learning models and algorithms.”

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Research#Topology🔬 ResearchAnalyzed: Jan 10, 2026 07:31

Research on $h$-topology in Rigid Spaces and p-adic Simpson Correspondence

Published:Dec 24, 2025 20:45
1 min read
ArXiv

Analysis

This article presents novel research in a specialized area of mathematics. The focus on $h$-topology within rigid spaces and its application to $p$-adic Simpson correspondence indicates a highly technical and niche contribution.
Reference

“The article's subject matter involves the $h$-topology for rigid spaces and its connection to the $p$-adic Simpson correspondence.”

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Research#llm🔬 ResearchAnalyzed: Jan 4, 2026 09:14

Around Segal conjecture in p-adic geometry

Published:Dec 19, 2025 15:10
1 min read
ArXiv

Analysis

This article likely discusses mathematical research related to the Segal conjecture within the framework of p-adic geometry. The title suggests an exploration or investigation of the conjecture, potentially offering new insights, proofs, or applications within this specific mathematical domain. The use of "Around" implies the article might not provide a definitive solution but rather contributes to the understanding of the conjecture.

Key Takeaways

    Reference

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