Related papers: Galois modules arising from Faltings's strict modu…

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…

We construct various explicit Herr complexes that compute the Galois cohomology of a $p$-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic $0$ with a perfect residue field of…

P. Aluffi introduced in [1] a new graded algebra in order to conveniently express characteristic cycles in the theory of singular varieties. This algebra is attached to a surjective ring homomorphism $A\surjects B$ by taking a suitable…

We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting operation which exchanges characteristic 0 and…

We obtain Fuchs decomposition theorem for regular singular differential modules over a large class of differential rings. We provide a definition of regularity inspired by differential Galois theory and we deduce the classical equivalence…

We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to…

We show that silting modules are closely related with localisations of rings. More precisely, every partial silting module gives rise to a localisation at a set of maps between countably generated projective modules and, conversely, every…

We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…

We describe the exact G-module F* for any cyclic extension F/K of locals fields of characteristic zero, where G is the Galois group of F/K. We also describe a parametrized space Wa,b,m,n which is most often a direct factor in F*.

We explain a derived version of the basic construction of localisations of module categories by means of idempotent ideals, which lie at the heart of Faltings' almost ring theory. We use it to provide an example of a commutative algebra in…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we…

It turns out that one can read off facts about schemes up to universal homeomorphism from their Galois categories. Here we propose a first modest slate of entries in a dictionary between the geometric features of a perfectly reduced scheme…

Recently an algebra of smooth valuations was attached to any smooth manifold. Roughly put, a smooth valuation is finitely additive measure on compact submanifolds with corners which satisfies some extra properties. In this note we initiate…

In this paper, by assuming a faithful action of a finite flat $\mathbb{Z}_p$-algebra $\mathscr{R}$ on a $p$-divisible group $\mathcal{G}$ defined over the ring of $p$-adic integers $\mathscr{O}_K$, we construct a category of new…

For a finite group scheme G over an algebraically closed field k of characteristic p>0 we study G-modules M, which are defined in terms of properties of their pull-backs along p-points of G. We show that the corresponding subcategories…

We study affine group schemes over a discrete valuation ring $R$ using two techniques: Neron blowups and Tannakian categories. We employ the theory developed to define and study differential Galois groups of $\mathcal D$-modules on a scheme…

Duality for complete discrete valuation fields with perfect residue field with coefficients in (possibly p-torsion) finite flat group schemes was obtained by Begueri, Bester and Kato. In this paper, we give another formulation and proof of…

In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…

In "On the calculation of some differential Galois groups" (Invent. Math. 87 (1987), no. 1), Katz defines the notion of a special flat connection on the complex affine line minus the origin, and he shows that the functor which restricts a…