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

Search: MSC category 11G15 ( Complex multiplication and moduli of abelian varieties [See also 14K22] )

 Expand all        Collapse all Results 1 - 5 of 5

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 functionCategories:14D07, 19F27, 33C20, 11G15, 14K22

2. CJM 2015 (vol 67 pp. 654)

Lim, Meng Fai; Murty, V. Kumar
 Growth of Selmer groups of CM Abelian varieties Let $p$ be an odd prime. We study the variation of the $p$-rank of the Selmer group of Abelian varieties with complex multiplication in certain towers of number fields. Keywords:Selmer group, Abelian variety with complex multiplication, $\mathbb{Z}_p$-extension, $p$-Hilbert class towerCategories:11G15, 11G10, 11R23, 11R34

3. CJM 2013 (vol 66 pp. 924)

Stankewicz, James
 Twists of Shimura Curves Consider a Shimura curve $X^D_0(N)$ over the rational numbers. We determine criteria for the twist by an Atkin-Lehner involution to have points over a local field. As a corollary we give a new proof of the theorem of Jordan-LivnÃ© on $\mathbf{Q}_p$ points when $p\mid D$ and for the first time give criteria for $\mathbf{Q}_p$ points when $p\mid N$. We also give congruence conditions for roots modulo $p$ of Hilbert class polynomials. Keywords:Shimura curves, complex multiplication, modular curves, elliptic curvesCategories:11G18, 14G35, 11G15, 11G10

4. CJM 2009 (vol 62 pp. 456)

Yang, Tonghai
 The ChowlaâSelberg Formula and The Colmez Conjecture In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form. Categories:11G15, 11F41, 14K22

5. CJM 2005 (vol 57 pp. 1102)

Weston, Tom
 Power Residues of Fourier Coefficients of Modular Forms Let $\rho \colon G_{\Q} \to \GL_{n}(\Ql)$ be a motivic $\ell$-adic Galois representation. For fixed $m > 1$ we initiate an investigation of the density of the set of primes $p$ such that the trace of the image of an arithmetic Frobenius at $p$ under $\rho$ is an $m$-th power residue modulo $p$. Based on numerical investigations with modular forms we conjecture (with Ramakrishna) that this density equals $1/m$ whenever the image of $\rho$ is open. We further conjecture that for such $\rho$ the set of these primes $p$ is independent of any set defined by Cebatorev-style Galois-theoretic conditions (in an appropriate sense). We then compute these densities for certain $m$ in the complementary case of modular forms of CM-type with rational Fourier coefficients; our proofs are a combination of the Cebatorev density theorem (which does apply in the CM case) and reciprocity laws applied to Hecke characters. We also discuss a potential application (suggested by Ramakrishna) to computing inertial degrees at $p$ in abelian extensions of imaginary quadratic fields unramified away from $p$. Categories:11F30, 11G15, 11A15
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2017 : https://cms.math.ca/