Related papers: Flat morphisms with regular fibers do not preserve…

We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…

We prove the following result. Let k be an infinite perfect field of positive characteristic and assume that strong resolution of singularities holds over k. Let R be a localization of a commutative d-dimensional k-algebra of finite type…

Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, in the following cases: --- The field k is p-special for some…

Let $R=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ of characteristic $p>0,$ let $\m=(x_1,..., x_n)$ be the maximal ideal generated by the variables, let $^*E$ be the naturally graded injective hull of $R/\m$ and let $^*E(n)$ be…

Let G be a connected linear algebraic group over an algebraically closed field k, and let H be a connected closed subgroup of G. We prove that the homogeneous variety G/H is a rational variety over k whenever H is solvable, or when dim(G/H)…

Hochster and Huneke showed that the property of F-regularity deforms for Gorenstein rings, i.e., if (R,m) is a Gorenstein local ring such that R/tR is F-regular for some nonzerodivisor t in m, then R is F-regular. This result was later…

Consider the (formal/analytic/algebraic) map-germs Maps(X,(k^p,o)). Let G be the group of right/contact/left-right transformations. I extend the following (classical) results from the real/complex-analytic case to the case of arbitrary…

In this paper we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings. One primary focus is the descent of these properties over…

Let X be a complex nonsingular affine algebraic variety, K a holomorphically convex subset of X, and Y a homogeneous variety for some complex linear algebraic group. We prove that a holomorphic map f:K-->Y can be uniformly approximated on K…

Let P be a commutative Noetherian ring, K be an ideal of P which is generated by a regular sequence of length four, f be a regular element of P, and Pbar be the hypersurface ring P/(f). Assume that K:f is a grade four Gorenstein ideal of P.…

Let $M\stackrel\pi \arrow X$ be a principal elliptic fibration over a Kaehler base $X$. We assume that the Kaehler form on $X$ is lifted to an exact form on $M$ (such fibrations are called positive). Examples of these are regular Vaisman…

Let $A$ be an abelian variety over a number field $K$. If $P$ and $Q$ are $K$-rational points of $A$ such that the order of the reduction of $Q$ divides that of $P$ for all but finitely many primes of the ring of integers of $K$, then there…

Let $I$ denote an ideal of a local ring $(R,\mathfrak{m})$ of dimension $n$. Let $M$ denote a finitely generated $R$-module. We study the endomorphism ring of the local cohomology module $H^c_I(M), c = \grade (I,M)$. In particular there is…

Let $k$ be a field with a real valuation $\nu$ and $R$ a $k$-algebra. We show that there exist a $k$-algebra $K$ and a real valuation $\mu$ on $K$ extending $\nu$ such that any real ring valuation of $R$ is induced by $\mu$ via some…

Let $D$ be an integrally closed local Noetherian domain of Krull dimension 2, and let $f$ be a nonzero element of $D$ such that $fD$ has prime radical. We consider when an integrally closed ring $H$ between $D$ and $D_f$ is determined…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the…

We prove that Z in definable in Q by a formula with 2 universal quantifiers followed by 7 existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that…

We prove a versions of amplitude inequalities of Iversen, Foxby and Iyengar, and Frankild and Sather-Wagstaff that replace finite generation conditions with adic finiteness conditions. As an application, we prove that a local ring $R$ of…

For a finitely generated module $M$, over a commutative Noetherian local ring $(R, \mathfrak{m})$, it is shown that there exist only a finite number of non--isomorphic top local cohomology modules $\mathrm{H}_{\mathfrak{a}}^{\mathrm{dim}…