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2 results on '"CM abelian variety"'

1. Nonvanishing of Hecke L-Functions for CM Fields and Ranks of Abelian Varieties.

Author

Masri, Riad and Yang, Tonghai

Subjects
*HECKE algebras, *GROUP algebras, *ABELIAN equations, *ABELIAN functions, *MORDELL conjecture, *ALGEBRAIC curves
Abstract

In this paper we prove a nonvanishing theorem for central values of L-functions associated to a large class of algebraic Hecke characters of CM number fields. A key ingredient in the proof is an asymptotic formula for the average of these central values. We combine the nonvanishing theorem with work of Tian and Zhang [] to deduce that infinitely many of the CM abelian varieties associated to these Hecke characters have Mordell-Weil rank zero. Included among these abelian varieties are higher-dimensional analogues of the elliptic $${{\mathbb Q}}$$ -curves A( D) of B. Gross []. [ABSTRACT FROM AUTHOR]

Published
2011
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2. Boundary components of mumford-tate domains

Author

Gregory Pearlstein and Matt Kerr

Subjects
Pure mathematics, Kato–Usui space, 20G99, General Mathematics, Boundary (topology), Fibered knot, 32G20, Mumford–Tate domain, 01 natural sciences, 17B45, 32M10, Mathematics - Algebraic Geometry, Mathematics::Algebraic Geometry, 0103 physical sciences, FOS: Mathematics, Limit (mathematics), Representation Theory (math.RT), 0101 mathematics, Algebraic Geometry (math.AG), Mathematics, Group (mathematics), 14D07, 010102 general mathematics, 14D07, 14M17, 17B45, 20G99, 32M10, 32G20, Nilpotent, limit mixed Hodge structure, boundary component, Mumford–Tate group, Astrophysics::Earth and Planetary Astrophysics, 010307 mathematical physics, Orbit (control theory), CM abelian variety, Mathematics - Representation Theory, 14M17, Hodge structure
Abstract

We study certain spaces of nilpotent orbits in Hodge domains, and treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit mixed Hodge structure of a generic such orbit. The result is used to present these spaces as iteratively fibered algebraic-group orbits in a minimal way. We conclude with two applications to variations of Hodge structure., 58 pages, 22 figures; final version, to appear in Duke Math. J.; section 6 substantially expanded

Published
2016

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