On Abelian extensions in mixed characteristic and ramification in codimension one
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910956107333632 |
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| author | Katz, Daniel Sridhar, Prashanth |
| author_facet | Katz, Daniel Sridhar, Prashanth |
| contents | A theorem of Paul Roberts states that the integral closure of a regular local ring in a generically abelian extension is Cohen-Macaulay, provided the characteristic of the residue field does not divide the order of the Galois group. An example of Koh shows the conclusion is false in the modular case. After a modification to the statement concerning ramification over $p$ in codimension one, we give an extension of Roberts's theorem to the modular case for unramified regular local rings in mixed characteristic when the $p$-torsion of the Galois group is annihilated by $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Abelian extensions in mixed characteristic and ramification in codimension one Katz, Daniel Sridhar, Prashanth Commutative Algebra Algebraic Geometry 13B05 A theorem of Paul Roberts states that the integral closure of a regular local ring in a generically abelian extension is Cohen-Macaulay, provided the characteristic of the residue field does not divide the order of the Galois group. An example of Koh shows the conclusion is false in the modular case. After a modification to the statement concerning ramification over $p$ in codimension one, we give an extension of Roberts's theorem to the modular case for unramified regular local rings in mixed characteristic when the $p$-torsion of the Galois group is annihilated by $p$. |
| title | On Abelian extensions in mixed characteristic and ramification in codimension one |
| topic | Commutative Algebra Algebraic Geometry 13B05 |
| url | https://arxiv.org/abs/2403.04972 |