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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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Research Paper#Category Theory, Group Theory🔬 ResearchAnalyzed: Jan 3, 2026 16:51

Polynomial Functors over Free Nilpotent Groups

Published:Dec 30, 2025 07:45
1 min read
ArXiv

Analysis

This paper investigates polynomial functors, a concept in category theory, applied to free nilpotent groups. It refines existing results, particularly for groups of nilpotency class 2, and explores modular analogues. The paper's significance lies in its contribution to understanding the structure of these mathematical objects and establishing general criteria for comparing polynomial functors across different degrees and base categories. The investigation of analytic functors and the absence of a specific ideal further expands the scope of the research.
Reference

“The paper establishes general criteria that guarantee equivalences between the categories of polynomial functors of different degrees or with different base categories.”

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Research Paper#AI Agents, Functional Programming, LLMs🔬 ResearchAnalyzed: Jan 3, 2026 16:29

Monadic Context Engineering for AI Agents

Published:Dec 27, 2025 01:52
1 min read
ArXiv

Analysis

This paper proposes a novel architectural paradigm, Monadic Context Engineering (MCE), for building more robust and efficient AI agents. It leverages functional programming concepts like Functors, Applicative Functors, and Monads to address common challenges in agent design such as state management, error handling, and concurrency. The use of Monad Transformers for composing these capabilities is a key contribution, enabling the construction of complex agents from simpler components. The paper's focus on formal foundations and algebraic structures suggests a more principled approach to agent design compared to current ad-hoc methods. The introduction of Meta-Agents further extends the framework for generative orchestration.
Reference

“MCE treats agent workflows as computational contexts where cross-cutting concerns, such as state propagation, short-circuiting error handling, and asynchronous execution, are managed intrinsically by the algebraic properties of the abstraction.”

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