It is with great sadness that the Institute learnt of Lucien Szpiro’s passing. A world-renowned researcher in commutative algebra, Diophantine geometry and arithmetic geometry, he defended his PhD at Paris-Sud University in 1971, under the supervision of Pierre Samuel. In his first works on commutative algebra, he obtained a solution of the Auslander conjecture and, together with Christian Peskine, developed the theory of liason on algebraic varieties. His interests then focused on Diophantine geometry, first for function fields and then in the case of number fields.
In the early 1980s, he was the first to realise the importance of a paper by Arakelov for questions of Diophantine geometry, and brought out a new subject that would have had a decisive impact on Faltings’ proof of the Mordell conjecture. He then showed the link between the positivity of the dualising sheaf of a curve and the Bogomolov conjecture. The latter states that the algebraic points of curves of genus at least 2 in the Neron-Tate topology of its Jacobian variety are discrete.
In 1981, Lucien Szpiro made a famous conjecture that compares discriminant and conductors of elliptic curves. An equivalent form of this statement is the “abc” conjecture, later proposed by Masser and Oesterlé, which remains a central question in number theory. More recently, Lucien Szpiro got interested in dynamical systems for Diophantine geometry.
After a short stay as an assistant professor in the Department of Science in Paris, Lucien Szpiro worked as a CNRS researcher between 1969 and 1999 at Jussieu, ENS Ulm and then at Paris-Sud University. He later held a professorship at the CUNY graduate center in New York.
At every stage of his career, he was able to gather an active group of researchers around himself and organised several memorable seminars and working groups. He also directed the thesis of 17 mathematicians including those of Shouwu Zhang, Laurent Moret-Bailly and of Ahmed Abbes and Emmanuel Ullmo, both now at IHES.
The mathematical community has lost a charismatic personality, the source of inspiration for a generation of arithmetic geometers. Our thoughts are with his wife Beth and his family.