4 papers
Algebraic vs. analytic: a survey
Aravind Asok, Tom Bachmann, Michael J. Hopkins
Given a pair of complex algebraic varieties, we can ask: does every analytic map admit an algebraic representative? Such questions are most interesting when the source and target a…
On P^1-stabilization in unstable motivic homotopy theory
Aravind Asok, Tom Bachmann, Michael J. Hopkins
We analyze stabilization with respect to in the Morel--Voevodsky unstable motivic homotopy theory. We introduce a refined notion of cellularity (a.k.a., biconnectiv…
-invariant motivic cohomology of schemes
Tom Bachmann, Elden Elmanto, Matthew Morrow
Voevodsky outlined a conjectural programme that his slice filtration in motivic homotopy theory should give rise to a good theory of -invariant motivic cohomology. Th…
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 o…