The pro-etale homotopy type |
Paul Meffle |
Freitag, 10. Januar 2025 10:30Uhr |
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After reviewing the classical construction of the etale homotopy type by Artin-Mazur we define a pro-etale analogue for the pro-etale site of a scheme. An important difference between the etale and pro-etale site of a scheme is that the latter has enough weakly contractible objects. Using this fact we prove that the pro-etale homotopy type of a qcqs scheme is determined by a single split affine weakly contractible hypercovering. Lastly and if time permits, we discuss the pro-etale homotopy type of a field. |