Finiteness of étale fundamental groups by reduction modulo $p$

Bhargav Bhatt; Ofer Gabber; Martin Olsson

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arXiv · 1705.07303

Finiteness of étale fundamental groups by reduction modulo $p$

Bhargav Bhatt·Ofer Gabber·Martin Olsson

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Abstract

We introduce a spreading out technique to deduce finiteness results for étale fundamental groups of complex varieties by characteristic $p$ methods, and apply this to recover a finiteness result proven recently for local fundamental groups in characteristic $0$ using birational geometry.

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Bhargav Bhatt, Ofer Gabber, Martin Olsson. 2017-05-20. Finiteness of étale fundamental groups by reduction modulo $p$. https://arxiv.org/abs/1705.07303

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