Related papers: Tannakian categories in positive characteristic

In the mid sixties, A. Grothendieck envisioned a vast generalization of Galois theory to systems of polynomials in several variables, motivic Galois theory, and introduced tannakian categories on this occasion. In characteristic zero,…

We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…

This exposition examines the theory of orthogonal groups and their subgroups over fields of positive characteristic, which has recently been used as an important tool in the study of automorphic forms and Langlands functionality. We present…

For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near…

We study higher jumping numbers and generalized test ideals associated to determinantal ideals over a field of positive characteristic. We work in positive characteristic and give a complete characterization of both families for ideals…

The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…

We give an account of model theory in the context of compactly generated triangulated and tensor-triangulated categories ${\cal T}$. We describe pp formulas, pp-types and free realisations in such categories and we prove elimination of…

We study the problem of deformation quantization for (algebraic) symplectic manifolds over a base field of positive characteristic. We prove a reasonably complete classification theorem for one class of such quantizations; in the course of…

Given an oligomorphic group $G$ and a measure $\mu$ for $G$ (in a sense that we introduce), we define a rigid tensor category $\underline{\mathrm{Perm}}(G; \mu)$ of "permutation modules," and, in certain cases, an abelian envelope…

This paper gives a survey on a valuation theoretical approach to local uniformization in positive characteristic, the model theory of valued fields in positive characteristic, and their connection with the valuation theoretical phenomenon…

We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in characteristic zero. We discuss the connection between the…

The Frobenius depth denoted by $\Fdepth$ defined by Hartshorne-Speiser in 1977 and later by Lyubeznik in 2006, in a different way, for rings of positive characteristic. The aim of the present paper is to compare the $\Fdepth$ with formal…

A characterization of positive operators on finite dimensional complex vector spaces based on the Routh-Hurwitz Criterion.

Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…

While the classification of univariate power series up to coordinate change is trivial in characteristic 0, this classification is very different in positive characteristic. In this note we give a complete classification of univariate power…

We study the space of non-degenerate traces on quantized Kleinian singularities of type A by studying their complement, the degenerate traces. In particular, we find the dimension of the space of twisted traces as a function of the…

The relevance that the property of complete positivity has had in the determination of quantum structures is briefly reviewed, together with recent applications to neutron optics and quantum Brownian motion. A possible useful application…

We define tensor categories ${\sf Ver}_{p^n}(G)$ in characteristic $p$ for connected reductive groups $G$ and positive integers $n$, generalising the semisimple Verlinde categories ${\sf Ver}_p(G)$ originating from Gelfand-Kazhdan and the…

In this paper, we conjecture an extension of the Hilbert basis theorem and the finite generation of invariants to commutative algebras in symmetric finite tensor categories over fields of positive characteristic. We prove the conjecture in…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…