Flat Regular Models of Elliptic Schemes

Flat Regular Models of Elliptic Schemes Synopsis

Measure Data and Numerical Schemes for Elliptic Problems

In order to show existence of solutions for linear elliptic problems with measure data, a first classical method, due to Stampacchia, is to use a duality argument (and a regularity result for elliptic problems). Another classical method is to pass to the limit on approximate solutions obtained with regular data (converging towards the measure data). A third method is presented. It consists to p...

On the Néron models of abelian surfaces with quaternionic multiplication

In this paper we construct a certain proper regular model for abelian surfaces with quaternionic multiplication. The construction applies when the residue characteristic p > 3 or more generally in the tamely ramified case. Our model has the property that the Néron model can be recovered as its smooth locus. We therefore obtain both the Néron model and a compactification of it. We are able to gi...

Arithmetic Moduli of Generalized Elliptic Curves

1.1. Motivation. In [DR], Deligne and Rapoport developed the theory of generalized elliptic curves over arbitrary schemes and they proved that various moduli stacks for (ample) “level-N” structures on generalized elliptic curves over Z[1/N ]-schemes are Deligne–Mumford stacks over Z[1/N ]. These stacks were proved to be Z[1/N ]-proper, and also finite flat over the Z[1/N ]-localization of the p...

Modular equations for Lubin-Tate formal groups at chromatic level 2

gives an equation for a curve that represents the moduli problem [Γ0(p)] for elliptic curves over a perfect field of characteristic p. This moduli problem associates to such an elliptic curve its finite flat subgroup schemes of rank p. A choice of such a subgroup scheme is equivalent to an isogeny from the elliptic curve with a prescribed kernel. The j-invariants of the source and target curves...