Related papers: Total $p$-differentials on schemes over $Z/p^2$

We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…

In this manuscript, we investigate the properties of systems formed by translations of an operator in the Schatten $p$-classes $\mathcal{T}^p$. We establish the existence of Schauder frames of integer translates in $\mathcal{T}^p$ for…

We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus…

We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension $F/\mathbb Q_p$, and an arbitrary finite…

We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…

In this paper, we establish the following family version of Habegger's bounded height theorem on abelian varieties: a locally closed subvariety of an abelian scheme with Gao's $t^{\mathrm{th}}$ degeneracy locus removed, intersected with all…

We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…

This paper develops two theories, the geometric theory of derived Grassmannians (and flag schemes) and the algebraic theory of derived Schur (and Weyl) functors, and establishes their connection, a derived generalization of the…

Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a derived category of Ind-coherent sheaves on a stack of…

Throughout our work on the L\^e cycles of an affine hypersurface singularity, our primary algebraic tool consisted of a method for taking the Jacobian ideal of a complex analytic function and decomposing it into pure-dimensional "pieces".…

Let G be a reductive group over the field F=k((t)), where k is an algebraic closure of a finite field, and let W be the (extended) affine Weyl group of G. The associated affine Deligne-Lusztig varieties $X_x(b)$, which are indexed by…

In this paper, we construct a class of $2$-dimensional formal groups over $\mathbb{Z}_p$ that provide a higher-dimensional analogue of the usual $1$-dimensional Lubin-Tate formal groups, then we initiate the study of the extensions…

We provide a uniform construction of "mixed versions" or "graded lifts" in the sense of Beilinson-Ginzburg-Soergel which works for arbitrary Artin stacks. In particular, we obtain a general construction of graded lifts of many categories…

For a given prime $p$, a new construction of families of the complex valued sequences of period $p$ with efficient implementation is given by applying both multiplicative characters and additive characters of finite field $\mathbb{F}_p$.…

Presenting p-adic numbers as {\em deformations} of finite fields allows a better understanding of Frobenius lifts and their connection with p-derivations in the sense of Buium \cite{Buium-Main}. In this way "numbers {\em are} functions", as…

We give conditions under which the number of solutions of a system of polynomial equations over a finite field F_q of characteristic p is divisible by p. Our setup involves the substitution t_i |-> f_i(t_i) for auxiliary polynomials…

We study oplax colimits of stable categories, of hermitian categories and of Poincar\'e categories in nice cases. This allows us to produce a categorical model of the assembly map of a bordism-invariant functor of Poincar\'e categories…

Let $p$ be a prime number and let $k$ be an algebraically closed field of characteristic $p$. A $BT_1$ group scheme over $k$ is a finite commutative group scheme which arises as the kernel of $p$ on a $p$-divisible (Barsotti--Tate) group.…

We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be…

Using aritmethic conditions on affine semigroups we prove that for a simplicial toric variety of codimension 2 the property of being a set-theoretic complete intersection on binomials in characteristic $p$ holds either for all primes $p$,…