Bibliographic Information: Kevin Lin and Wyatt Reeves. (2024). Coherent Sheaves, Sheared D-Modules, and Hochschild Cochains. arXiv:2410.10692v1 [math.AG].
Research Objective: This paper aims to investigate the microlocal geometry of coherent sheaves from a categorical perspective, focusing on the relationship between sheared D-modules, Hochschild cochains, and the category of singularities.
Methodology: The authors utilize advanced techniques from derived algebraic geometry, category theory, and microlocal analysis. They leverage the theory of singular support, Koszul duality, and the HKR theorem to establish their main results.
Key Findings:
Main Conclusions: The established Morita equivalence provides a powerful tool for studying the microlocal geometry of coherent sheaves and their relationship to D-modules and Hochschild cohomology. The results have significant implications for understanding the geometric Langlands conjecture and the theory of Arthur parameters.
Significance: This research significantly advances the understanding of the interplay between algebraic geometry, representation theory, and microlocal analysis. The categorical framework developed in this paper provides new tools and insights for tackling challenging problems in these fields.
Limitations and Future Research: While the paper focuses on quasi-smooth schemes and stacks, extending these results to more general settings, including formal stacks, remains an open question. Further exploration of the connections between this work and the Langlands program, particularly in the context of Arthur parameters, is a promising avenue for future research.
To Another Language
from source content
arxiv.org
Key Insights Distilled From
by Kevin Lin, W... at arxiv.org 10-15-2024
https://arxiv.org/pdf/2410.10692.pdfDeeper Inquiries