Title: Unramified Brauer Group and Its Applications
Subjects: Associative algebras, Associative rings, Geometry, algebraic, Brauer groups, Cohomology operations, Associative rings and algebras, Division rings and semisimple Artin rings, Algebraic geometry, Birational geometry, Rationality questions, Special varieties, Rational and unirational varieties, Arithmetic problems. Diophantine geometry, Rational points, Group theory and generalizations, Connections with homological algebra and category theory, Cohomology of groups, Field theory and polynomials, Homological methods (field theory), Galois cohomology, Associative rings and algebras -- Division rings and semisimple Artin rings -- Brauer groups, Algebraic geometry -- Birational geometry -- Rationality questions, Algebraic geometry -- Special varieties -- Rational and unirational varieties, Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points, Group theory and generalizations -- Connections with homological algebra and category theory -- Cohomology of groups, Field theory and polynomials -- Homological methods (field theory) -- Galois cohomology