A variant of Néron models over curves

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...

Néron models and compactified Picard schemes over the moduli stack of stable curves

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

The Néron Model over the Igusa Curves

We analyze the geometry of rational p-division points in degenerating families of elliptic curves in characteristic p. We classify the possible Kodaira symbols and determine for the Igusa moduli problem the reduction type of the universal curve. Special attention is paid to characteristic 2 and 3 where wild ramification and stacky phenomena show up.

Lecture 9: Néron models