Rob de Jeu教授学术报告

报告题目：Bloch groups and tessellations of hyperbolic 3-space

报告人：Rob de Jeu 教授

报告人单位： 荷兰 Vrije Universiteit

报告时间：2019年8月26日，上午10:00-11:00

报告地点：四牌楼校区逸夫建筑馆1502

报告摘要：

Let k be an imaginary quadratic number field with ring of integers R. We discuss how an ideal tessellation of hyperbolic 3-space on which GL_2(R) acts gives rise to an explicit element b of infinite order in the second Bloch group for k, and hence to an element c in K_3(k) modulo torsion, which is cyclic of infinite order.  The regulator of c equals -24 \zeta_k'(-1), and the Lichtenbaum conjecture for k at -1 implies that a generator of K_3(k) modulo torsion can be obtained by dividing c by twice the order of K_2(R). (The Lichtenbaum conjecture at 0, because of the functional equation, amounts to the classical formula for the residue at s=1 of the zeta-function, involving the regulator of R^*=K_1(R), the size of the torsion subgroup of R^*, and the class number of R.)

This division could be carried out explicitly in several cases by dividing b in the second Bloch group.  The most notable case is that of Q(\sqrt{-303}), where K_2(R) has order~22.

This is joint work with David Burns, Herbert Gangl, Alexander Rahm, and Dan Yasaki.

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