53 citations · 300 across the 40 of their papers we have counts for
42 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…
Splitting vector bundles over real algebraic varieties
Aravind Asok, Jean Fasel, Samuel Lerbet
Suppose is a smooth affine real variety and is a vector bundle over . We analyze the problem of splitting off a free rank one summand from in cor…
Efficient generation of projective modules: a motivic view
Aravind Asok, Morgan Opie, Brian Shin +1
Assume is a field and is a smooth -algebra of dimension . If is a projective module of rank , then it is well-known that can be generated by -elements…
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…
Constructing projective modules
Aravind Asok
We discuss elements of a social history of the theory of projective modules over commutative rings. We attempt to study the question: how did the theory of projective modules becom…
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…