论文标题
Abelian表面和非Archimedean Hodge d conjocture-半稳定案例
Abelian surfaces and the non-Archimedean Hodge D-conjecture -- the semi-stable case
论文作者
论文摘要
如果$ x $是$ {\ mathbb r} $的平滑投射品种，则hodge $ {\ mathcal d} $ - beilinson的猜想声明了调节器地图的溢流性，可以使用真实的系数deligne共同体。众所周知，它通常是错误的，但在某些特殊情况下是正确的，例如Abelian表面和$ K3 $ -SURFACES，并且当在数字字段上定义品种时，仍然期望是正确的。我们证明了这种类似物的类似物，即在表面降低不良的非架构场所的阿贝尔表面。在这里，Deligne的共同体被特殊纤维的某个Chow组取代。减少良好的情况更加困难，并且在椭圆曲线的产物和一般情况下，首先是由Spiess研究的。
If $X$ is a smooth projective variety over ${\mathbb R}$, the Hodge ${\mathcal D}$-conjecture of Beilinson asserts the surjectivity of the regulator map to Deligne cohomology with real coefficients. It is known to be false in general but is true in some special cases like Abelian surfaces and $K3$-surfaces - and still expected to be true when the variety is defined over a number field. We prove an analogue of this for Abelian surfaces at a non-Archimedean place where the surface has bad reduction. Here the Deligne cohomology is replaced by a certain Chow group of the special fibre. The case of good reduction is harder and was first studied by Spiess in the case of products of elliptic curve and by me in general.
