Semistable reduction of modular curves associated with maximal subgroups in prime level
Language
en
Article de revue
This item was published in
Doc.Math. 2021, vol. 26, p. 231
English Abstract
We complete the description of semistable models for modular curves associated with maximal subgroups of $\mathrm{GL}_2 ({\mathbb F}_p )$ (for $p$ any prime, $p>5$). That is, in the new cases of non-split Cartan modular ...Read more >
We complete the description of semistable models for modular curves associated with maximal subgroups of $\mathrm{GL}_2 ({\mathbb F}_p )$ (for $p$ any prime, $p>5$). That is, in the new cases of non-split Cartan modular curves and exceptional subgroups, we identify the irreducible components and singularities of the reduction mod $p$, and the complete local rings at the singularities. We review the case of split Cartan modular curves. This description suffices for computing the group of connected components of the fibre at $p$ of the Néron model of the Jacobian.Read less <
English Keywords
modular
singularity
Cartan
exceptional
fibre
stability
11G18
11G20
14G35 (sec- ondary)
Origin
Hal imported