Pierre Deligne is a Belgian mathematician who was a student of Alexander Grothendieck, then worked at l’IHÉS and now is emeritus at IAS.
publication list (pdf)
list of scanned articles: numdam
Luc Illusie, From Pierre Deligne’s secret garden: looking back at some of his letters (pdf)
Deligne’s main interests include algebraic geometry especially cohomology of algebraic varieties, Hodge theory, L-functions and automorphic forms, Tannakian theory, representation theory 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.
On Deligne-Mumford stacks and the example of the moduli space of curves:
On differential equations with regular singular points (and developing local systems, twisted cohomology, twisted de Rham cohomology, Gauss-Manin connections):
Introducing Deligne cohomology in complex analytic geometry (by a chain complex of holomorphic differential forms) with applications to Hodge theory and intermediate Jacobians:
On elliptic curves over general commutative ground rings (in arithmetic geometry):
On the Weil conjectures:
On rational homotopy theory of Kähler manifolds:
Pierre Deligne, Phillip Griffiths, John Morgan, Dennis Sullivan, Real homotopy theory of Kähler manifolds, Invent Math (1975) 29: 245 (doi:10.1007/BF01389853)
(containing the statement that the co-binary Sullivan differential is the dual Whitehead product)
On perverse sheaves:
On tensor categories and Tannaka duality
culminating in Deligne's theorem on tensor categories:
Deligne led a seminar on differential systems corresponding to meromorphic connections, whose basic results were explained in a classic in this are:
Related to this is the survey
Last revised on June 8, 2022 at 15:28:51. See the history of this page for a list of all contributions to it.