论文标题
蒙福德（Mumford Tate
Mumford-Tate groups of 1-motives and Weil pairing
论文作者
论文摘要
我们展示了1-动力$ M $的几何形状（即内态存在的存在以及定义点之间的关系）确定其动机Galois组$ {\ Mathcal {\ Mathcal {g}} {\ Mathrm {al}}}} _ {\ Mathrm {\ Mathrm {\ Mathrm {\ Matrm {Mot {Mot}}（m）$。固定周期矩阵$π_m$和$π_{m^*} $分别与1-Motive $ m $相关联，以及与Cartier Dual $ m^*，我们描述了这些矩阵上$ M $的动作。在半纤维化案例中，根据$ m $的几何形状，我们对$ m $的周期之间的多项式关系进行了分类，我们对代表$ M $的Mumford-Tate组的矩阵进行了详尽的计算。如果1-动作，这种表示形式对Grothendieck时期的猜想带来了新的启示。
We show how the geometry of a 1-motive $M$ (that is existence of endomorphisms and relations between the points defining it) determines the dimension of its motivic Galois group ${\mathcal{G}}{\mathrm{al}}_{\mathrm{mot}}(M)$. Fixing periods matrices $Π_M$ and $Π_{M^*}$ associated respectively to a 1-motive $M$ and to its Cartier dual $M^*,$ we describe the action of the Mumford-Tate group of $M$ on these matrices. In the semi-elliptic case, according to the geometry of $M$ we classify polynomial relations between the periods of $M$ and we compute exhaustively the matrices representing the Mumford-Tate group of $M$. This representation brings new light on Grothendieck periods conjecture in the case of 1-motives.
