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math.AG2023
On multi-graded Proj schemes
Arnaud Mayeux, Simon Riche
We review the construction (due to Brenner--Schröer) of the Proj scheme associated with a ring graded by a finitely generated abelian group. This construction generalizes the well-…
math.AG2023
A survey on algebraic dilatations
Adrien Dubouloz, Arnaud Mayeux, João Pedro dos Santos
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturall…
math.AG2023
Multi-centered dilatations, congruent isomorphisms and Rost double deformation space
Arnaud Mayeux
We introduce multi-centered dilatations of rings, schemes and algebraic spaces, a basic algebraic concept. Dilatations of schemes endowed with a structure (e.g. monoid, group or Li…