Tohoku Mathematical Journal

$0$-cycles on the elliptic modular surface of level $4$

Andreas Langer

Full-text: Open access

Article information

Tohoku Math. J. (2), Volume 50, Number 2 (1998), 291-302.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C10
Secondary: 11G35: Varieties over global fields [See also 14G25] 14C25: Algebraic cycles 14J27: Elliptic surfaces


Langer, Andreas. $0$-cycles on the elliptic modular surface of level $4$. Tohoku Math. J. (2) 50 (1998), no. 2, 291--302. doi:10.2748/tmj/1178224979.

Export citation


  • [B] S BLOCK, Lectures on algebraic cycles, Duke Univ Math Series, Durham 1980
  • [J] U. JANNSEN, On the /-adic cohomology of varieties over number fields and its Galois cohomology, in: Galois groups over, Math Sci Res Inst Publ 16, Springer-Verlag, New York 1989, 315-360
  • [L] A LANGER, Local points of motives in semistable reduction, to appear in Compositio Mathematica
  • [L-R] A LANGER AND W. RASKIND, 0-cycles on the selfproduct of a CM-elliptic curve over Q, preprin 1996
  • [L-S] A LANGER AND S. SAITO, Torsion zero-cycles on the selfproduct of a modular elliptic curve, in Duke Math J 85 no 2 (1996), 415-447
  • [Mi] S. MILDENHALL, Cycles in a product of elliptic curves, and a group analogous to the class group, Duke Math J 67 (1992), 387-406
  • [M-S] A S MERKURJEV AND A. SUSLIN, -cohomology of Severi-Brauer varieties and the norm residu homomorphism, Math USSR Izv 21 (1983), 307-340
  • [Shi] T SHIODA, Algebraic cycles on certain 3-surfaces in char p, in: Manifolds, Tokyo 1973, 357-364, ed by A. Hattori, Univ of Tokyo Press, Tokyo, 1975
  • [W] A WILES, Modular elliptic curves and Fermat's last theorem, Annals of Math142 (1995), 443-551