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Explore the practical applications of ℓ-adic cohomology theory in this advanced mathematical lecture delivered at the International Conference on Birational and Symplectic geometry 2025, where Philippe Michel demonstrates how this powerful algebraic tool from arithmetic geometry can be applied to solve concrete problems in number theory and algebraic geometry, covering the fundamental constructions of ℓ-adic cohomology groups, their key properties including comparison theorems and trace formulas, and showcasing specific examples where these techniques provide insights into Diophantine equations, modular forms, and the arithmetic of algebraic varieties over finite fields.
