Multi-centered dilatations and congruent isomorphisms
Résumé
We introduce a multi-centered formalism in the context of dilatations of schemes and algebraic spaces. In particular, this provides new results on the behavior of [MRR20] dilatations. Furthermore, we use our new formalism to deduce some refined congruent isomorphisms. Contents 1 Introduction 1 2 Dilatations of semirings 5 3 Multi-centered dilatations in the absolute setting 14 4 Iterated multi-centered dilatations 21 5 Multi-centered dilatations along multiples of a single divisor 24 6 Some flatness and smoothness results 26 7 Néron blowups 27 8 Congruent isomorphisms 29 References 30 Acknowledgement.