Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: MSC category 11G55 ( Polylogarithms and relations with \$K\$-theory )

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2006 (vol 58 pp. 419)

Snaith, Victor P.
 Stark's Conjecture and New Stickelberger Phenomena We introduce a new conjecture concerning the construction of elements in the annihilator ideal associated to a Galois action on the higher-dimensional algebraic \$K\$-groups of rings of integers in number fields. Our conjecture is motivic in the sense that it involves the (transcendental) Borel regulator as well as being related to \$l\$-adic \'{e}tale cohomology. In addition, the conjecture generalises the well-known Coates--Sinnott conjecture. For example, for a totally real extension when \$r = -2, -4, -6, \dotsc\$ the Coates--Sinnott conjecture merely predicts that zero annihilates \$K_{-2r}\$ of the ring of \$S\$-integers while our conjecture predicts a non-trivial annihilator. By way of supporting evidence, we prove the corresponding (conjecturally equivalent) conjecture for the Galois action on the \'{e}tale cohomology of the cyclotomic extensions of the rationals. Categories:11G55, 11R34, 11R42, 19F27

© Canadian Mathematical Society, 2015 : https://cms.math.ca/