Abstract
We prove that the oo-category of motivic spectra satisfies Milnor excision: if A B is a morphism of commutative rings sending an ideal I C A isomorphically onto an ideal of B, then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A/I that are identified over B/IB. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We ...
Abstract
We prove that the oo-category of motivic spectra satisfies Milnor excision: if A B is a morphism of commutative rings sending an ideal I C A isomorphically onto an ideal of B, then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A/I that are identified over B/IB. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub's etale motives over schemes of finite virtual cohomological dimension.
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