Conservativity conjecture: Ayoub notes

From Joseph Ayoub’s talk in the workshop last week “The conservativity conjecture for Chow motives in characteristic zero” ayoub-conservativity-conj-notes

More at Ayoub’s website

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de Jeu talk tomorrow

Rob de Jeu. Thursday, January 24, 14:30 @HIM

(Rob’s website)

Title: Tessellations, Bloch groups, homology groups

Abstract:

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^ind(k), which is cyclic of infinite order. The regulator of c equals -12 \zeta_k'(-1), and the Lichtenbaum conjecture for k at -1 implies that a generator of K_3^ind(k) can be obtained by dividing c by the
order of K_2(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.