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2 results

  • THE BRAUER–MANIN OBSTRUCTION FOR ZERO-CYCLES ON SEVERI–BRAUER FIBRATIONS OVER CURVES

  • JOOST VAN HAMEL
  • Journal:
    Journal of the London Mathematical Society / Volume 68 / Issue 2 / October 2003
    Published online by Cambridge University Press:
    25 September 2003, pp. 317-337
    Print publication:
    October 2003

  • Introducing the framework of pseudo-motivic homology, the paper finishes the proof that the Brauer–Manin obstruction is the only obstruction to the local–global principle for zero-cycles on a Severi–Brauer fibration of squarefree index over a smooth projective curve over a number field, provided that the Tate–Shafarevich group of the Jacobian of the base curve is finite. More precisely, for such a variety the Chow group of global zero-cycles is dense in the subgroup of collections of local cycles that are orthogonal to the (cohomological) Brauer group of the variety.

  • Algebraic cycles and topology of real Enriques surfaces

  • FRÉDÉRIC MANGOLTE, JOOST VAN HAMEL
  • Journal:
    Compositio Mathematica / Volume 110 / Issue 2 / January 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 215-238
    Print publication:
    January 1998
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  • For a real Enriques surface $Y$ we prove that every homology class in $H_1(Y(R), Z/2)$ can be represented by a real algebraic curve if and only if all connected components of $Y(R)$ are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface $Y$.