2018/08/28 by Misha Gavrilovich, Gavrilovich, Misha
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1808.09332
openalex publication_date 2018/08/28 · openalex created_date 2018/09/07 · openalex updated_date 2026/07/28
We formulate two conjectures about etale cohomology and fundamental groups motivated by categoricity conjectures in model theory. One conjecture says that there is a unique Z-form of the etale cohomology of complex algebraic varieties, up to Aut(C)-action on the source category; put differently, each comparison isomorphism between Betti and etale cohomology comes from a choice of a topology on C. Another conjecture says that each functor to groupoids from the category of complex algebraic varieties which is similar to the topological fundamental groupoid functor, in fact factors through it, up to a field automorphism of the complex numbers acting on the category of complex algebraic varieties. We also try to present some evidence towards these conjectures, and show that some special cases seem related to Grothendieck standard conjectures and conjectures about motivic Galois group.