Decomposition theorem for semi-simples

TL;DR

This paper extends the decomposition and hard Lefschetz theorems in algebraic geometry to broader contexts without requiring quasi-projectivity, using advanced homological algebra techniques.

Contribution

It generalizes key theorems in algebraic geometry, removing the quasi-projectivity assumption through new algebraic and geometric constructions.

Findings

Theorems hold without quasi-projectivity assumptions.

Extensions apply to broader classes of algebraic varieties.

Maintains validity of decomposition and Lefschetz theorems in new settings.

Abstract

We use standard constructions in algebraic geometry and homological algebra to extend the decomposition and hard Lefschetz theorems of T. Mochizuki and C. Sabbah so that they remains valid without the quasi-projectivity assumptions.