Semiorthogonal decomposition

Semiorthogonal decomposition is a concept in mathematics, particularly in the fields of functional analysis and category theory. It refers to a method of breaking down a complex structure into simpler components that satisfy certain orthogonality conditions. In a more specific context, particularly in algebraic geometry and derived categories, semiorthogonal decomposition allows the decomposition of a category—typically a derived category of coherent sheaves—into simpler subcategories that have a well-defined relationship with each other.