This paper initiates the incorporation of factorization algebra techniques to study motivic homot... more This paper initiates the incorporation of factorization algebra techniques to study motivic homotopy theory. We define a version of the Ran space of an algebraic variety and prove that it is contractible in the unstable motivic homotopy category. To do so, we prove that its A 1-homotopy sheaves vanish, the most difficult being the sheaf of A 1-connected components where we use an interpretation of this sheaf, available in the setting of infinite fields and a Riemann-Roch argument.
This paper initiates the incorporation of factorization algebra techniques to study motivic homot... more This paper initiates the incorporation of factorization algebra techniques to study motivic homotopy theory. We define a version of the Ran space of an algebraic variety and prove that it is contractible in the unstable motivic homotopy category. To do so, we prove that its A 1-homotopy sheaves vanish, the most difficult being the sheaf of A 1-connected components where we use an interpretation of this sheaf, available in the setting of infinite fields and a Riemann-Roch argument.
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Papers by Elden Elmanto