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math.AG2025
Unstable motivic and real-étale homotopy theory
Aravind Asok, Tom Bachmann, Elden Elmanto +1
We prove that for any base scheme , real étale motivic (unstable) homotopy theory over coincides with unstable semialgebraic topology over (that is, sheaves of spaces on…
math.AG2018
Towards conservativity of -stabilization
Tom Bachmann, Maria Yakerson
We study the interplay of the homotopy coniveau tower, the Rost-Schmid complex of a strictly homotopy invariant sheaf, and homotopy modules. For a strictly homotopy invariant sheaf…
math.AG2017
Motivic equivalence of affine quadrics
Tom Bachmann, Alexander Vishik
In this article we show that the motive of an affine quadric {q = 1} determines the respective quadratic form.