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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12402 |
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| _version_ | 1866911333125980160 |
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| author | Shen, Wanchun |
| author_facet | Shen, Wanchun |
| contents | We study the relationship between higher Du Bois singularities and $K$-regularity, a notion that measures the $\mathbb{A}^1$-invariance of the algebraic $K$-groups. Building on this relationship, we establish a strengthened form of Vorst's conjecture for local complete intersections in characteristic zero. Our work also provides tools to construct new examples that illustrate various phenomena in the study of $K$-regularity. The main inputs for our results are vanishing theorems for the Du Bois complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On higher Du Bois singularities and $K$-regularity Shen, Wanchun Algebraic Geometry K-Theory and Homology We study the relationship between higher Du Bois singularities and $K$-regularity, a notion that measures the $\mathbb{A}^1$-invariance of the algebraic $K$-groups. Building on this relationship, we establish a strengthened form of Vorst's conjecture for local complete intersections in characteristic zero. Our work also provides tools to construct new examples that illustrate various phenomena in the study of $K$-regularity. The main inputs for our results are vanishing theorems for the Du Bois complexes. |
| title | On higher Du Bois singularities and $K$-regularity |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2504.12402 |