Related papers: Coefficient fields and scalar extension in positiv…

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. We prove that if $D$ has a constant positive scalar curvature K\"{a}hler metric, $X \setminus D$ admits…

Let $K$ be a global or local field, $E/K$ a Galois extension, and Br$(E)$ the Brauer group of $E$. This paper shows that if $K$ is a local field, $v$ is its natural discrete valuation, $v'$ is the valuation of $E$ extending $v$, and $q$ is…

Let \(K\) be a perfectoid field with pseudo-uniformizer \(\pi\). We adapt an argument of Du in \cite{DuUncountable} to show that the perfectoid Tate algebra \(K\langle x^{1 / p^{\infty}} \rangle\) has an uncountable chain of distinct prime…

Let $K$ be a field of characteristic zero and suppose that $f:\mathbb{N}\to K$ satisfies a recurrence of the form $$f(n)\ =\ \sum_{i=1}^d P_i(n) f(n-i),$$ for $n$ sufficiently large, where $P_1(z),...,P_d(z)$ are polynomials in $K[z]$.…

For a class of linear maps on a von Neumann factor, we associate two objects, bounded operators and trace class operators, both of which play the roles of Choi matrices. Each of them is positive if and only if the original map on the factor…

Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of fractions. Under the assumption that K contains all r-th roots of unity for an integer r, we prove that, given an…

Let E be a field of characteristic p. In a previous paper of ours, we defined and studied super-H\"older vectors in certain E-linear representations of Z_p. In the present paper, we define and study super-H\"older vectors in certain…

We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…

Let $k$ be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the {\L}ojasiewicz exponent…

Let $K$ be a global field of positive characteristic. Let $\infty$ be a fixed place of $K$. This paper gives an explicit isomorphism between the space of automorphic forms (resp. cusp forms) for $GL_{n+1}(K)$ that transform like the special…

Let $K/F$ be a finite Galois extension of number fields. It is well known that the Tchebotarev density theorem implies that an irreducible, finitely ramified $p$-adic representation $\rho$ of the absolute Galois group of $K$ is determined…

Let $G$ be a reductive group over a field $k$ of characteristic $\neq 2$, let ${\mathfrak g}=\Lie(G)$, let $\theta$ be an involutive automorphism of $G$ and let ${\mathfrak g}={\mathfrak k}\oplus{\mathfrak p}$ be the associated symmetric…

A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…

Let $X$ be a closed equidimensional local complete intersection subscheme of a smooth projective scheme $Y$ over a field, and let $X_t$ denote the $t$-th thickening of $X$ in $Y$. Fix an ample line bundle $\mathcal{O}_Y(1)$ on $Y$. We prove…

The Fourier coefficients F(t) of a function f on a compact symmetric space U/K are given by integration of f against matrix coefficients of irreducible representations of U. The coefficients depend on a spectral parameter t, which…

In this paper, for a field $k$ of characteristic zero and a finitely generated $k$-algebra $R$, we give a set of generators for the image ideals of irreducible nice and quasi-nice $R$-derivations on the polynomial ring $R[X,Y]$, where $R$…

It is well known that the Tchebotarev density theorem implies that an irreducible $\ell$-adic representation $\rho$ of the absolute Galois group of a number field $K$ is determined (up to isomorphism) by the characteristic polynomials of…

We show that each local field $\mathbb{F}_q((t))$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most $1$ by (certain small quotients of) its absolute Galois group…

Let k be an algebraically closed field and A be a finite-dimensional associative basic k-algebra of the form A=kQ/I where Q is a quiver without oriented cycles or double arrows and I is an admissible ideal of kQ. We consider roots of the…

In this paper we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field K.