The Splitting Lemma in any Characteristic
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911267357196288 |
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| author | Greuel, Gert-Martin Pfister, Gerhard |
| author_facet | Greuel, Gert-Martin Pfister, Gerhard |
| contents | We give a simple proof of the splitting lemma in singularity theory, also known as generalized Morse lemma, for formal power series over arbitrary fields. Our proof for the uniqueness of the residual part in any characteristic is new and was previously unknown in characteristic two. Beyond the formal case, we give proofs for algebraic power series and for convergent real and complex analytic power series, which are new for non-isolated singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Splitting Lemma in any Characteristic Greuel, Gert-Martin Pfister, Gerhard Algebraic Geometry 14B05, 14B07, 14B12 We give a simple proof of the splitting lemma in singularity theory, also known as generalized Morse lemma, for formal power series over arbitrary fields. Our proof for the uniqueness of the residual part in any characteristic is new and was previously unknown in characteristic two. Beyond the formal case, we give proofs for algebraic power series and for convergent real and complex analytic power series, which are new for non-isolated singularities. |
| title | The Splitting Lemma in any Characteristic |
| topic | Algebraic Geometry 14B05, 14B07, 14B12 |
| url | https://arxiv.org/abs/2507.17078 |