Related papers: Dependent Artin-Schreier Defect Extensions and Str…
We prove the logarithmic extension theorem for one-forms on strongly $F$-regular singularities. Additionally, we establish the logarithmic extension theorem for one-forms on three-dimensional klt singularities in characteristic $p>41$. To…
We present here a version of the Artin-Schreier polynomial that works in any characteristic. Let $C_p$ be the cyclic group of prime order $p$. Equivalently, we prove one can lift degree $p$ cyclic $C_p$ extensions over local rings $R,M$…
We describe two crystal structures on set-valued decomposition tableaux. These provide the first examples of interesting "$K$-theoretic" crystals on shifted tableaux. Our first crystal is modeled on a similar construction of Monical,…
Let F be a characteristic zero differential field with an algebraically closed field of constants, E be a no-new-constant extension of F by antiderivatives of F and let y1, ..., yn be antiderivatives of E. The antiderivatives y1, ..., yn of…
We introduce $t$-Hermitian forms of arbitrary degree $k$, a natural extension of classical degree $k$ Hermitian forms obtained through a synthesis of the tensor transformation law and the $t$-product of third-order tensors. We show that…
Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and Stark systems over principal artinian rings and discrete valuation rings. In this article we describe a natural extension of (a slightly modified version of)…
We show that certain products of Whittaker functions and Schwartz functions on a general linear group extend to Whittaker functions on a larger general linear group. This generalizes results of Cogdell--Piatetski-Shapiro \cite{CPS} and…
The purpose of this article is to extend the earliest results of A.A. Brudno, connecting topological entropy of a subshift X over $\mathbb{N}$ to the Kolmogorov complexity of words in X, to subshifts over computable groups that posses…
We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an expander, confirming a conjecture due to Wigderson and Xiao. Our proof is based on a new multi-matrix extension of the Golden-Thompson…
In this paper, we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Riemann hypothesis. This extends the previously known bounds…
Chiral conformal blocks in a rational conformal field theory are a far going extension of Gauss hypergeometric functions. The associated monodromy representations of Artin's braid group capture the essence of the modern view on the subject,…
We consider deformations of a differential system with Poincare' rank 1 at infinity and Fuchsian singularity at zero along a stratum of a coalescence locus. We give necessary and sufficient conditions for the deformation to be strongly…
Correlators in monomial Hermitian matrix model strongly depend on the choice of eigenvalue integration contours. We express Schur correlator in case of several different integration contours (mixed phase case) as a sum over products of…
We show that the Kuratowski imbedding of a Riemannian manifold in L^\infty, exploited in Gromov's proof of the systolic inequality for essential manifolds, admits an approximation by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional…
We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…
We establish precise regularity conditions for $L_p$-boundedness of Fourier multipliers in the group algebra of $SL_n(\mathbf{R})$. Our main result is inspired by H\"ormander-Mikhlin criterion from classical harmonic analysis, although it…
We introduce the notion of extension of 1-motives. Using the dictionary between strictly commutative Picard stacks and complexes of abelian sheaves concentrated in degrees -1 and 0, we check that an extension of 1-motives induces an…
We study the extension theory for the two-dimensional first-order system $Ju' +qu = wf$ of differential equations on the real interval $(a,b)$ where $J$ is a constant, invertible, skew-hermitian matrix and $q$ and $w$ are matrices whose…
We use Artin-Schreier base change to construct counterexamples to a Kummer-Vandiver type question for function fields.
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…