Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Descent of algebraic cycles

Pages: 135 – 154

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n1.a7


Johannes Anschütz (Mathematisches Institut, Universität Heidelberg, Germany)


We characterize universally generalizing morphisms which satisfy descent of algebraic cycles as those which are surjective with generically reduced fibres. In doing so, we introduce a naive pullback of cycles for arbitrary morphisms between noetherian schemes, which generalizes the classical pullback for flat morphisms, and then prove basic properties of this naive pullback.


algebraic cycle, descent

2010 Mathematics Subject Classification


Published 6 June 2017