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René Schoof (born 8 May 1955, Den Helder)〔(R.J. Schoof, 1955 - ) at the University of Amsterdam ''Album Academicum'' website〕 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'').〔〔(René Schoof, Mathematics Genealogy Project )〕 He is now a professor at the University Tor Vergata in Rome.〔(R. Schoof's homepage, University Tor Vergata )〕 In 1985, Schoof discovered an algorithm which enabled him to count points on elliptic curves over finite fields in polynomial time.〔René Schoof: ''Elliptic curves over finite fields and the calculation of square roots mod p'', Mathematics of Computation, No. 44, 1985, 483–494.〕 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 == * Schoof's algorithm * Schoof–Elkies–Atkin algorithm 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「René Schoof」の詳細全文を読む スポンサード リンク
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