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4 papers · 2 filters
Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields
Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann +3
We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. In particular, we show t…
Droites sur les hypersurfaces cubiques
Jean-Louis Colliot-Thélène
Over any complex cubic hypersurface of dimension at least 2, the Chow group of 1-dimensional cycles is spanned by the lines lying on the hypersurface. The smooth case has already b…
Stability conditions on Kuznetsov components
Arend Bayer, Martí Lahoz, Emanuele Macrì +1
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland…
On function field Mordell-Lang: the semiabelian case and the socle theorem
Franck Benoist, Elisabeth Bouscaren, Anand Pillay
We here aim to complete our model-theoretic account of the function field Mordell-Lang conjecture, avoiding appeal to dichotomy theorems for Zariski geometries, where we now consid…