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Stable homotopy theory over general base schemes

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If you have a question about this talk, please contact Andreas Holmstrom.

In the 90s, Morel and Voevodsky invented motivic (or A1-) homotopy theory for algebraic varieties, importing many techniques from algebraic topology into algebraic geometry. More recently, Ayoub generalised this to much more general schemes, and Deglise and Cisinski used Ayoub’s machinery to realize part of Beilinson’s dream of “mixed motivic sheaves”. In this survey talk we will define motives and the motivic stable homotopy category over a general base scheme and discuss some of their properties.

This talk is part of the Motivic stable homotopy theory study group series.

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