Abstract: We continue the study ofn-dependent groups, fields and related structures, largely motivated by the conjecture that everyn-dependent field is dependent. We provide evidence toward this conjecture by showing that every infiniten-dependent valued field of positive characteristic is henselian, obtaining a variant of Shelah’s Henselianity Con...
Published in Selecta Mathematica
A major open problem in the theory of twisted commutative algebras (tca’s) is proving noetherianity of finitely generated tca’s. For bounded tca’s this is easy; in the unbounded case, noetherianity is only known for Sym(Sym2(C∞))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepa...
We give an explicit recursive description of the Hilbert series and Gröbner bases for the family of quadratic ideals defining the jet schemes of a double point. We relate these recursions to the Rogers–Ramanujan identity and prove a conjecture of the second author, Oblomkov and Rasmussen.
We study a class of tame theories $T$ of topological fields and their extension $T_{\delta}^*$ by a generic derivation. The topological fields under consideration include henselian valued fields of characteristic 0 and real closed fields. For most examples, we show that the associated expansion by a generic derivation has the open core property (i....
AbstractWe prove that every ultraproduct of p-adics is inp-minimal (i.e., of burden 1). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued fields of equicharacteristic 0 in the RV language.
We introduce a symmetric operad whose algebras are the Operator Product Expansion (OPE) Algebras of quantum fields. There is a natural classical limit for the algebras over this operad and they are commutative associative algebras with derivations. The latter are the algebras of classical fields. In this paper we completely develop our approach to ...
We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as an analogue of stable monomial ideals within the class of monomial ideals. We show that a symmetr...
In this paper we present a matricial result that generalizes Hironaka's game and Perron transforms simultaneously. We also show how one can deduce the various forms in which the algorithm of Perron appears in proofs of local uniformization from our main result.
Published in Semigroup Forum
A simple way of computing the Apéry set of a numerical semigroup (or monoid) with respect to a generator, using Groebner bases, is presented, together with a generalization for affine semigroups. This computation allows us to calculate the type set and, henceforth, to check the Gorenstein condition which characterizes the symmetric numerical subgro...
In this paper we discuss how seemingly different notions of locality and causality in quantum field theory can be unified using a non-abelian generalization of the Hammerstein property (originally introduced as a weaker version of linearity). We also prove a generalization of the main theorem of renormalization, in which we do not require field ind...
