The abelian fundamental group with modulus in mixed characteristic
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914108933144576 |
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| author | Ooe, Ryosuke |
| author_facet | Ooe, Ryosuke |
| contents | We define the abelian fundamental group with modulus of a regular flat scheme over a discrete valuation ring, taking into account wild ramification along a divisor. Our definition provides a mixed-characteristic analogue of the abelian fundamental group with modulus introduced by Kerz--Saito for smooth schemes over a perfect field. In this setting, we prove a Lefschetz-type theorem for strictly semi-stable schemes: restriction to a hypersurface of sufficiently large degree relative to the ramification induces an isomorphism of the abelian fundamental groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The abelian fundamental group with modulus in mixed characteristic Ooe, Ryosuke Algebraic Geometry 14H30, 11S15 We define the abelian fundamental group with modulus of a regular flat scheme over a discrete valuation ring, taking into account wild ramification along a divisor. Our definition provides a mixed-characteristic analogue of the abelian fundamental group with modulus introduced by Kerz--Saito for smooth schemes over a perfect field. In this setting, we prove a Lefschetz-type theorem for strictly semi-stable schemes: restriction to a hypersurface of sufficiently large degree relative to the ramification induces an isomorphism of the abelian fundamental groups. |
| title | The abelian fundamental group with modulus in mixed characteristic |
| topic | Algebraic Geometry 14H30, 11S15 |
| url | https://arxiv.org/abs/2510.20138 |