Realizations of Biextensions

Biextensions of 1-motives by 1-motives

Let S be a scheme. In this paper, we define the notion of biextensions of 1-motives by 1-motives. If M(S) denotes the Tannakian category generated by 1-motives over S (in a geometrical sense), we define geometrically the morphisms of M(S) from the tensor product of two 1-motives M_1 and M_2 to another 1-motive M_3, to be the isomorphism classes of biextensions of (M_1,M_2) by M_3. Generalizing this definition we obtain, modulo isogeny, the geometrical notion of morphism of M(S) from a finite tensor product of 1-motives to another 1-motive.

局部高度对的渐进行为

Asymptotics of local height pairing

研究局部高度对的渐进行为，通过同调代数和Deligne上同调方法比较不同双延伸构造，扩展了Beilinson的Hodge上同调理论。

Multilinear morphisms between 1-motives

Let S be an arbitrary scheme. We define biextensions of 1-motives by 1-motives which we see as the geometrical origin of morphisms from the tensor product of two 1-motives to a third one. If S is the spectrum of a field of characteristic 0, we check that these biextensions define morphisms from the tensor product of the realizations of two 1-motives to the realization of a third 1-motive. Generalizing we obtain the geometrical notion of morphisms from a finite tensor product of 1-motives to another 1-motive.

Hecke特征标与Picard曲面的Eisenstein上同调的Bloch-Beilinson猜想

Bloch-Beilinson conjectures for Hecke characters and Eisenstein cohomology of Picard surfaces

本文研究Hecke特征标与Picard曲面的Eisenstein上同调之间的Bloch-Beilinson猜想，通过构造Hodge结构延伸并计算双延伸高度来验证其非平凡性。