René Schoof
| René Schoof | |
|---|---|
| File:Rene Schoof.jpg | |
| Born | René J. Schoof May 8, 1955 Den Helder, Nederland |
| Nationality | Dutch |
| Fields | Mathematics |
| Institutions | University of Rome Tor Vergata |
| Alma mater | University of Amsterdam |
| Doctoral advisor | Hendrik W. Lenstra Jr. |
René Schoof (born 8 May 1955, Den Helder)[1] is a mathematician from the Netherlands who works in Algebraic Number Theory, Arithmetic Algebraic Geometry, Computational Number Theory and Coding Theory.
He received his Ph.D. in 1985 from the University of Amsterdam with Hendrik Lenstra (Elliptic Curves and Class Groups).[1][2] He is now a professor at the University Tor Vergata in Rome.[3]
In 1985, Schoof discovered an algorithm which enabled him to count points on elliptic curves over finite fields in polynomial time.[4] This was important for the use of elliptic curves in cryptography, and represented a theoretical breakthrough, as it was the first deterministic polynomial time algorithm for counting points on elliptic curves. The algorithms known before (e.g. the baby-step giant-step algorithm) were of exponential running time. His algorithm was improved by A. O. L. Atkin (1992) and Noam Elkies (1990).
He obtained the best known result extending Deligne's Theorem for finite flat group schemes to the non commutative setting, over certain local Artinian rings. His interests range from Algebraic Number Theory, Arakelov theory, Iwasawa theory, problems related to existence and classification of Abelian varieties over the rationals with bad reduction in one prime only, algorithms.
He also wrote a book on Catalan's conjecture.
See also
External links
Some publications
- Counting points of elliptic curves over finite fields, Journal des Théories des Nombres de Bordeaux, No. 7, 1995, 219–254, pdf
- With Gerard van der Geer, Ben Moonen (editors): Number fields and function fields – two parallel worlds, Birkhäuser 2005
- Finite flat group schemes over Artin rings, Compositio Mathematica, v. 128 (2001), 1–15
- Catalan´s Conjecture, Universitext, Springer, 2008
References
- ↑ 1.0 1.1 R.J. Schoof, 1955 - at the University of Amsterdam Album Academicum website
- ↑ René Schoof, Mathematics Genealogy Project
- ↑ R. Schoof's homepage, University Tor Vergata
- ↑ René Schoof: Elliptic curves over finite fields and the calculation of square roots mod p, Mathematics of Computation, No. 44, 1985, 483–494.
