论文标题
洛朗田地的合理连接品种上的零周期
Zero cycles on rationally connected varieties over Laurent fields
论文作者
论文摘要
我们研究了具有代数封闭残基磁场的特征性零laurent场定义的合理连接的品种上的零周期。我们表明，该度图引发了在此类领域定义的合理连接的三倍的同构。通常，如果在特征零的代数闭合场中定义的合理连接的品种，则度图是一个同构，可以满足一个周期的积分hodge/tate构想，或者如果在有限磁场上定义的表面上的除法类别对tate stustoxture是正确的。为了证明这些结果，我们介绍了最小模型计划中的技术，以研究Kato/Bloch-Ogus定义的某些复合物的同源性。
We study zero cycles on rationally connected varieties defined over characteristic zero Laurent fields with algebraically closed residue fields. We show that the degree map induces an isomorphism for rationally connected threefolds defined over such fields. In general, the degree map is an isomorphism if rationally connected varieties defined over algebraically closed fields of characteristic zero satisfy the integral Hodge/Tate conjecture for one cycles, or if the Tate conjecture is true for divisor classes on surfaces defined over finite fields. To prove these results, we introduce techniques from the minimal model program to study the homology of certain complexes defined by Kato/Bloch-Ogus.
