# nLab Pierre Deligne

Pierre Deligne is a Belgian mathematician who was a student of Grothendieck, then worked at l’IHÉS and now is emeritus at IAS. His main interests include algebraic geometry especially cohomology of algebraic varieties, Hodge theory, L-functions and automorphic forms, Tannakian theory, representations of algebraic groups, and motives, where he extended the conjectural picture from pure to mixed motives (Grothendieck was much earlier aware and pushing toward that extension, though not publishing about it, according to Serre and others). Deligne has obtained the Fields medal in 1978 for a famous 1973 proof of Weil conjectures. For the sake of preparatory/foundational steps he wrote a quick amendement for the unfinished volumes of SGA in a form of practical and short (but controversial to Grothendieck) SGA $4\frac{1}{2}$. This work uses a powerful and deep yoga of Hodge filtrations discovered also by Deligne.

• Luc Illusie, From Pierre Deligne’s secret garden : looking back at some of his letters (pdf)

## Writings

Deligne lead a seminar on differential systems corresponding to meromorphic connections, whose basic results were explained in a classic in this are:

• Équations différentielles à points singuliers réguliers, Lect. Notes in Math. 163, Springer-Verlag (1970)

Related to this is the survey

With David Mumford, he wrote the historical article on Deligne-Mumford stacks at the principal example of the moduli space of curves.

• P. Deligne, D. Mumford, The irreducibility of the space of curves of a given genus Publ. Math. de l’IHÉS 36 (1969) pp. 75–109, numdam.

• A. A. Beilinson, J. Bernstein, P. Deligne, Faisceaux pervers, Astérisque 100 (1983).

• La conjecture de Weil : I, Publications Mathématiques de l’IHÉS 43 (1974), p. 273-307 numdam