Timeline for Component group of Neron model of a parametrized abelian variety

6 events

when toggle format	what		by	license	comment
Dec 18, 2012 at 19:50	comment	added	David Corwin		It seems that I wasn't reading carefully enough. My question is actually answered in the paragraph after Theorem 3.2.2 in Ribet's thesis.
Jul 26, 2012 at 21:35	comment	added	Xarles		And observe that your last coment is directly related to what I did together with Siegfried Bosch in the paper Component groups of Néron models via rigid uniformization, Math. Ann. Volume 306, Number 1 (1996), 459-486.
Jul 26, 2012 at 21:32	comment	added	Xarles		I don't understand exactly what is the question, but observe that the component group of the Neron model is isomorphic (as abstract group) to the cokernel of the map given by the valuation matrix (from $\mathbb{Z}^2$ to itself). This is shown, if I remember well, in the SGA7, Expose IX, and it is due to Raynaud.
Jul 16, 2012 at 21:39	comment	added	Will Sawin		Since $GL_2(\mathbb Z)$ acts on your matrix on the right without changing the geometry of the abelian variety, only the image of the matrix should carry geometric meaning. In particular the quotient of $\mathbb Z^2$ by the image of the valuation matrix should be the group of components. This would follow from the fact that $\mathcal O_K^{\times} \times \mathcal O_K^{\times}$ is the group of sections which have good reduction at $0$, that is, lie in the identity component.
Jul 16, 2012 at 21:26	history	edited	Will Sawin	CC BY-SA 3.0	added 10 characters in body
Jul 16, 2012 at 19:27	history	asked	David Corwin	CC BY-SA 3.0