On the behavior of stringy motives under Galois quasi-étale covers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866918068330954752 |
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| author | Carvajal-Rojas, Javier Yasuda, Takehiko |
| author_facet | Carvajal-Rojas, Javier Yasuda, Takehiko |
| contents | We investigate the behavior of stringy motives under Galois quasi-étale covers. We prove that they descend under such covers in a sense defined via their Poincaré realizations. Further, we show that such descent is strict in the presence of ramification. As a corollary, we reduce the problem regarding the finiteness of the étale fundamental group of KLT singularities to a DCC property for their stringy motives. We verify such DCC property for surfaces in arbitrary characteristic. As an application, we give a characteristic-free proof for the finiteness of the étale fundamental group of log terminal surface singularities, which was unknown in equal characteristics 2 and 3 and in mixed characteristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05214 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the behavior of stringy motives under Galois quasi-étale covers Carvajal-Rojas, Javier Yasuda, Takehiko Algebraic Geometry 14E30, 14E20, 14E18, 14B05 We investigate the behavior of stringy motives under Galois quasi-étale covers. We prove that they descend under such covers in a sense defined via their Poincaré realizations. Further, we show that such descent is strict in the presence of ramification. As a corollary, we reduce the problem regarding the finiteness of the étale fundamental group of KLT singularities to a DCC property for their stringy motives. We verify such DCC property for surfaces in arbitrary characteristic. As an application, we give a characteristic-free proof for the finiteness of the étale fundamental group of log terminal surface singularities, which was unknown in equal characteristics 2 and 3 and in mixed characteristics. |
| title | On the behavior of stringy motives under Galois quasi-étale covers |
| topic | Algebraic Geometry 14E30, 14E20, 14E18, 14B05 |
| url | https://arxiv.org/abs/2105.05214 |