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Search: MSC category 19F27 ( Etale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10] )

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1. CJM Online first

Asakura, Masanori; Otsubo, Noriyuki
CM periods, CM Regulators and Hypergeometric Functions, I
We prove the Gross-Deligne conjecture on CM periods for motives associated with $H^2$ of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the $K_1$-regulators in terms of hypergeometric functions ${}_3F_2$, and obtain a new example of non-trivial regulators.

Keywords:period, regulator, complex multiplication, hypergeometric function
Categories:14D07, 19F27, 33C20, 11G15, 14K22

2. 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

3. CJM 2000 (vol 52 pp. 47)

Chinburg, T.; Kolster, M.; Snaith, V. P.
Comparison of $K$-Theory Galois Module Structure Invariants
We prove that two, apparently different, class-group valued Galois module structure invariants associated to the algebraic $K$-groups of rings of algebraic integers coincide. This comparison result is particularly important in making explicit calculations.

Categories:11S99, 19F15, 19F27

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