Michel Raynaud (16 June 1938 – 10 March 2018) was a French mathematician who made lasting contributions to algebraic and arithmetic geometry. He held a professorship at Université Paris‑Sud (Paris‑Sud 11) and worked on problems linking geometry, number theory and Galois groups. His work combined geometric ideas with arithmetic methods to resolve questions about algebraic curves, abelian varieties and fundamental groups.

Major results and significance

Raynaud is best known for two landmark achievements that influenced subsequent research in arithmetic geometry. In 1983 he published a proof of the Manin–Mumford conjecture, a statement about torsion points on subvarieties of abelian varieties. Later he shared the 1995 Frank Nelson Cole Prize in Algebra with David Harbater for contributions leading to the solution of the Abhyankar conjecture, a problem concerning which finite groups occur as Galois groups of branched covers of the affine line over fields of positive characteristic.

Methods and themes

Throughout his career Raynaud employed techniques from several areas: algebraic geometry (models, reductions and moduli), arithmetic geometry (reduction mod p and specialization), and the study of fundamental groups. His proofs often combined delicate geometric constructions with arithmetic specialization arguments. These methods influenced later work on diophantine geometry and the study of rational and torsion points on varieties.

Awards and recognition

  • Prize Ampère of the Académie des Sciences (1987)
  • Frank Nelson Cole Prize in Algebra (1995), shared with David Harbater

These honors reflect the international importance of his solutions to problems that had been open for decades.

Legacy and further reading

Raynaud's results remain standard references in courses and research on arithmetic geometry and the geometry of abelian varieties. For biographical notes, publication lists and obituary notices see a university profile or institutional remembrances such as the professional profile, an academic announcement at host institution, and contemporaneous obituaries and retrospectives at scholarly outlets: retrospective and obituary notice. He died in Paris on 10 March 2018 at age 79.

Selected topics linked to his work include:

  • Manin–Mumford conjecture (torsion in abelian varieties)
  • Abhyankar conjecture (Galois groups and branched covers)
  • Reduction and specialization techniques in arithmetic geometry