Commutative algebra Abelian categories Abelian varieties and schemes Algebra Algebra, Homological Arithmetic rings and other special rings Associative rings and algebras Associative rings and algebras -- Representation theory of rings and algebras -- Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers Associative rings and algebras -- Representation theory of rings and algebras -- Cohen-Macaulay modules Associative rings and algebras -- Representation theory of rings and algebras -- Representation type (finite, tame, wild, etc.) Associative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings Birational geometry Categories and geometry Category theory Cluster algebras.-msc Cohen-Macaulay modules Cohomology theory.-msc Commutative algebra -- Local rings and semilocal rings -- Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) Commutative algebra -- Ring extensions and related topics -- Étale and flat extensions; Henselization; Artin approximation Commutative algebra -- Theory of modules and ideals -- Cohen-Macaulay modules Commutative algebra -- Theory of modules and ideals -- Module categories Commutative algebra -- Theory of modules and ideals -- Structure, classification theorems Compact Riemann surfaces and uniformization.-msc Connections with combinatorics.-msc Functions of a complex variable Geometry, Algebraic Grothendieck groups.-msc Group theory and generalizations Homological dimension.-msc Homological methods