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Fitting ideals of ℓ-adic realizations of Picard 1-motives and class groups of global function fields
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Cornelius Greither
and
Cristian D. Popescu
Published/Copyright:
February 22, 2012
Abstract
In previous work, we proved a result on the equivariant Fitting ideal of the ℓ-adic realization of the Picard 1-motive attached to an abelian covering of curves defined over a finite field. In this paper, we build upon this work to deduce results on the equivariant Fitting ideal of the Tate modules of the Jacobian of the top curve, and on the equivariant Fitting ideal of the (dual of the) degree zero class group of the top curve. At the end, we discuss refinements of Brumer's conjecture and consider examples.
Received: 2010-09-08
Revised: 2011-06-01
Published Online: 2012-02-22
Published in Print: 2013-02
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Curve counting theories via stable objects Ⅱ : DT/ncDT flop formula
- Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions
- n-angulated categories
- Hypertrees, projections, and moduli of stable rational curves
- Locally conformally flat quasi-Einstein manifolds
- Annihilating Selmer modules
- Fitting ideals of ℓ-adic realizations of Picard 1-motives and class groups of global function fields
