Arnaud Mayeux

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20242026

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math.AG2026

Algebraic Magnetism: $X$ -products of attractors via $F_{1}$ -geometry

Arnaud Mayeux

We give a formula for $X$ -products of attractors using $F_{1}$ -geometry.

math.AG2025

Algebraic Magnetism

Arnaud Mayeux

For a diagonalizable monoid scheme $A (M)_{S}$ acting on an algebraic space $X$ , we introduce for any submonoid $N$ of $M$ an attractor space $X^{N}$ . We then investigate and study vari…

math.AG2025

On multi-graded Proj schemes

Arnaud Mayeux, Simon Riche

We review the construction (due to Brenner--SchrÃ¶er) of the Proj scheme associated with a ring graded by a finitely generated abelian group. This construction generalizes the well…

math.AG2024

A polyptych of multi-centered deformation spaces

Adrien Dubouloz, Arnaud Mayeux

Extending Verdier's deformation space to the normal cone of a closed subscheme and Rost's double deformation space of a pair of nested closed subschemes, we introduce a notion of d…

math.AG2024

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…

math.AG2024

A survey on algebraic dilatations

Adrien Dubouloz, Arnaud Mayeux, JoÃ£o 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…

Algebraic Magnetism: X-products of attractors via F1​-geometry

Algebraic Magnetism

On multi-graded Proj schemes

A polyptych of multi-centered deformation spaces

Multi-centered dilatations, congruent isomorphisms and Rost double deformation space

A survey on algebraic dilatations

Algebraic Magnetism: $X$ -products of attractors via $F_{1}$ -geometry