Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.11027 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913741117849600 |
|---|---|
| author | De Clercq, Charles Florence, Mathieu |
| author_facet | De Clercq, Charles Florence, Mathieu |
| contents | Let $p$ be a prime. In this article, we prove the Smoothness Theorem, which asserts that a $(1,1)$-cyclotomic pair is $(n,1)$-cyclotomic, for all $n \geq 1$. In the particular case of Galois cohomology, the Smoothness Theorem provides a new proof of the Norm Residue Isomorphism Theorem, entirely disjoint from motivic cohomology. A byproduct of this approach, is that the latter Theorem follows from mod $p^2$ Kummer theory for fields alone. We moreover extend it, from absolute Galois groups of fields, to algebraic fundamental groups of (not necessarily smooth, nor proper) curves over algebraically closed fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_11027 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Smooth profinite groups, III: the Smoothness Theorem De Clercq, Charles Florence, Mathieu Algebraic Geometry Let $p$ be a prime. In this article, we prove the Smoothness Theorem, which asserts that a $(1,1)$-cyclotomic pair is $(n,1)$-cyclotomic, for all $n \geq 1$. In the particular case of Galois cohomology, the Smoothness Theorem provides a new proof of the Norm Residue Isomorphism Theorem, entirely disjoint from motivic cohomology. A byproduct of this approach, is that the latter Theorem follows from mod $p^2$ Kummer theory for fields alone. We moreover extend it, from absolute Galois groups of fields, to algebraic fundamental groups of (not necessarily smooth, nor proper) curves over algebraically closed fields. |
| title | Smooth profinite groups, III: the Smoothness Theorem |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2012.11027 |