Related papers: Definable sets, motives and p-adic integrals

In this note we show that groups with definable generics in a separably closed valued of finite imperfection degree can be embedded into groups definable in their algebraic closure.

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…

For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [20]. This result…

We construct derived fundamental group schemes for Tate motives over connected smooth schemes over fields. We show that there exists a pro affine derived group scheme over the rationals such that its category of perfect representations…

We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…

In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

Let K be a valued field of characteristic p>0 with non-p-divisible value group. We show that every finite embedding problem for K whose kernel is a p-group is properly solvable.

Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…

We determine the nature of the fixed point sets of groups of order p, acting on complexes of distinguished p-subgroups (those p-subgroups containing p-central elements in their centers). The case when G has parabolic characteristic p is…

Fix a base field F, a finite field K and consider a sequence of central simple F-algebras A_1,...,A_n. In this note we provide some results toward a classification of the indecomposable motives lying in the motivic decompositions of…

The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.

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…

There are several remarks on Hilbert series of finitely presented (f. p.) associative algebras over a field and their modules. First, given an integer $D$, the set of Hilbert series of right-sided ideals with generators and relations of…

We prove an additivity for evenly (oddly) finite dimensional objects in distinguished triangles in a triangulated monoidal category structured by an underlying model monoidal category. In particular, the result holds in the Q-localized…

We discuss the deep relationship between $\infty$-categorical functional analysis and the anticipated theory of $p$-adic motives. The motivation fundamentally comes from applications essentially in arithmetics from very broad perspectives.…

Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…

Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over finite fields of characteristic not 2 and over finite…

We prove that for p-optimal fields (a very large subclass of p-minimal fields containing all the known examples) a cell decomposition theorem follows from methods going back to Denef's paper [Invent. Math, 77 (1984)]. We derive from it the…

In this paper we show that two dimensional (mod p) Galois representations satisfying mild hypotheses can be lifted to p-adic Galois representations ramified at infinitely many primes such that the characteristic polynomials of Frobenius at…