Jasper's Homepage


Address:

Jasper Scholten
COSIC/ESAT, K.U. Leuven
Kasteelpark Arenberg 10
3001 Leuven-Heverlee
Belgium
Room number: 01.66
Email: Jasper dot Scholten at esat dot kuleuven dot be
Phone: +32-16-321073
Fax: +32-16-321969

Research Interests

I am a mathematician. My research area is arithmetic algebraic geometry and number theory. I like to study both theoretical and computational aspects of these subjects. I wrote my undergraduate thesis on a computational problem in algebraic number theory. As a graduate student I did research on the arithmetic of elliptic curves and elliptic surfaces, and on Galois representations. After I finished my thesis my research on Galois representations extended to the modular forms side, related to the Langlands program. I also started to do research on zetafunctions of curves over finite fields. At the moment my research focusses on applications of elliptic and hyperelliptic curves to cryptography.

Preprints

  • Weil restriction of an elliptic curve over a quadratic extension. postscript pdf
  • Cover attacks. (with Claus Diem) A report for the AREHCC project. pdf
  • An Attack on a Trace-Zero Cryptosystem. (with Claus Diem). postscript
  • Ordinary elliptic curves of high rank over Fp(x) with constant j-invariant II. (with Claus Diem). postscript

    Papers

  • Mordell-Weil groups of elliptic surfaces and Galois representations (Thesis) postscript pdf.
  • Arithmetic on a quintic threefold (with C. Consani). International Journal of Mathematics, Vol.12, No.8 (2001) 943-972. postscript pdf.
  • Hyperelliptic curves in characteristic 2 (with H. Zhu). Inter. Math. Research Notices, 17 (2002), 905-917. postscript pdf.
  • First slope case of Wan's conjecture (with H. Zhu). Finite Fields and their Appl. 8 (2002), no. 4, 414-419. postscript pdf.
  • Slope estimates on Artin-Schreier curves (with H. Zhu). Compositio Mathematica 137 (2003), no. 3, 275-292. postscript pdf.
  • Families of supersingular curves in characteristic 2 (with H. Zhu). Mathematical Research Letters 9, no 5-6, 2002. Page 639. postscript pdf.
  • Ordinary elliptic curves of high rank over Fp(x) with constant j-invariant (with I. Bouw and C. Diem). Manuscripta Mathematica 114, 487-501 (2004) postscript pdf.


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