Resumen de Tame-wild dichotomy for coalgebras

Daniel Simson

• The concepts of a K-coalgebra C of tame comodule type and of wild comodule type over an algebraically closed field K are introduced in Simson [Colloq. Math. 90 (2001) 101�150] and basic properties of tame coalgebras and wild coalgebras are established in Simson [Colloq. Math. 90 (2001) 101�150; Lect. Notes Pure Appl. Math. 236 (2004) 465�492; J. Pure Appl. Algebra 202 (2005) 118�132; J. Algebra 312 (2007) 455�494]. Unfortunately, the tame�wild dichotomy theorem is proved only for a relatively narrow class of coalgebras. In the present paper, we introduce the concepts fc-tame coalgebra and fc-wild coalgebra, and we prove that any Homcomputable coalgebra over an algebraically closed field K is either fc-tame or fc-wild. Hence we conclude that the usual tame�wild dichotomy holds for semiperfect coalgebras