Néron Models

Lecture 9: Néron models

Néron models over moduli of stable curves

We construct Deligne-Mumford stacks Pd,g representable over Mg parametrizing Néron models of Jacobians as follows. Let K = k(B) be a one-dimensional function field and let XK be a smooth genus-g curve over K admitting stable minimal model over B. The Néron model N(PicXK) −→ B is the base change of Pd,g via the moduli map B −→ Mg of f , that is: N(Pic XK) ∼= Pd,g ×Mg B. Pd,g is compactified by a...

NÉRON MODELS AND COMPACTIFIED PICARD SCHEMES OVER THE MODULI STACK OF STABLE CURVES By LUCIA CAPORASO

We construct modular Deligne-Mumford stacks Pd,g representable over Mg parametrizing Néron models of Jacobians as follows. Let B be a smooth curve and K its function field, let XK be a smooth genus-g curve over K admitting stable minimal model over B. The Néron model N(PicXK ) → B is then the base change of Pd,g via the moduli map B −→ Mg of f , i.e.: N(PicXK ) ∼= Pd,g ×Mg B. Moreover Pd,g is c...

A Generalization of the Néron Models of Green, Griffiths and Kerr

We generalize a construction of the Néron model for a family of intermediate Jacobians due to Green, Griffiths and Kerr by using the theory of mixed Hodge modules. It is a topological group defined over any partial compactification of the base space, and it ‘graphs’ admissible normal functions. Moreover, there is a stratification of the partial compactification such that the restriction over ea...

THE FORMAL COMPLETION OF THE NÉRON MODEL OF Jo (p)

THE FORMAL COMPLETION OF THE NÉRON MODEL OF Jo (p)

Trace Formula for Component Groups of Néron Models

We study a trace formula for tamely ramified abelian varieties A over a complete discretely valued field, which expresses the Euler characteristic of the special fiber of the Néron model of A in terms of the Galois action on the l-adic cohomology of A. If A has purely additive reduction, the trace formula yields a cohomological interpretation for the number of connected components of the specia...