2024/06/06 by Sofía Marlasca Aparicio, Aparicio, Sofía Marlasca
Mathematics · #14A30 #18A40 #18C15 #54H13 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2406.04063
openalex publication_date 2024/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solid modules over ℚ or \mathbbFp, introduced by Clausen and Scholze, are a well-behaved variant of complete topological vector spaces that forms a symmetric monoidal Grothendieck abelian category. For a discrete field k, we construct the category of ultrasolid k-modules, which specialises to solid modules over ℚ or \mathbbFp. In this setting, we show some commutative algebra results like an ultrasolid variant of Nakayama's lemma. We also explore higher algebra in the form of animated and 𝔼_∞ ultrasolid k-algebras, and their deformation theory. We focus on the subcategory of complete profinite k-algebras, which we prove is contravariantly equivalent to equal characteristic formal moduli problems with coconnective tangent complex.