2019/03/07 by Raedschelders, Theo, Stevenson, Greg · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1903.02849
We prove that every proper connective DG-algebra A admits a geometric realization (as defined by Orlov) by a smooth projective scheme with a full exceptional collection. As a corollary we obtain that A is quasi-isomorphic to a finite dimensional DG-algebra and in the smooth case we compute the noncommutative Chow motive of A. We go on to analyse the relationship between smoothness and regularity in more detail as well as commenting on smoothness of the degree zero cohomology for smooth proper connective DG-algebras.