标题： ε常数和阿拉克尔OV欧拉特征 显示英文标题

标题： Epsilon constants and Arakelov Euler characteristics

摘要： 我们猜想，Hasse-Weil L函数在Z上的流形X的函数方程中的常数的绝对值的对数等于X的Arakelov de Rham欧拉特征。 这一猜想推广了数域的zeta函数在函数方程中的常数是其整数环的判别式的平方根这一事实。 我们证明这个猜想等价于Bloch猜想，该猜想将导子表示为微分的局部化陈类的次数。 我们在“良好”约化的情况下证明了这两个猜想。 显示英文摘要

摘要： We conjecture that the logarithm of the absolute value of the constant in the functional equation of the Hasse-Weil L-function of a variety X over Z is equal to a certain Arakelov de Rham Euler characteristic of X. This generalizes the fact that the constant in the functional equation of the zeta function of a number field is the square root of the discriminant of its ring of integers. We show that this conjecture is equivalent to Bloch's conjecture which expresses the conductor as the degree of a localized Chern class of the differentials. We prove both of these conjectures in the case of "tame" reduction.