Revisiting the determinacy on New Keynesian Models

The goal of this paper is to shed light on the determinacy question that arises in New Keynesian models as result of a combination of several monetary policy rules; in these models, we provide conditions to guarantee existence and uniqueness of equilibrium by means of results that are obtained from theoretical analysis. In particular, we show that Taylor--like rules in interest rate setting are not the only way to reach determinacy of the rational expectations equilibrium in the New Keynesian setting. The key technical tool that we use for that purposes is the so--called Budan--Fourier Theorem, that we review along the paper.Comment: 16 pages, comments are welcom

The level of pairs of polynomials

Given a polynomial $f$ with coefficients in a field of prime characteristic $p$, it is known that there exists a differential operator that raises $1/f$ to its $p$th power. We first discuss a relation between the `level' of this differential operator and the notion of `stratification' in the case of hyperelliptic curves. Next we extend the notion of level to that of a pair of polynomials. We prove some basic properties and we compute this level in certain special cases. In particular we present examples of polynomials $g$ and $f$ such that there is no differential operator raising $g/f$ to its $p$th power.Comment: 14 pages, comments are welcom

An algorithm for constructing certain differential operators in positive characteristic

Given a non-zero polynomial $f$ in a polynomial ring $R$ with coefficients in a finite field of prime characteristic $p$, we present an algorithm to compute a differential operator $\delta$ which raises $1/f$ to its $p$th power. For some specific families of polynomials, we also study the level of such a differential operator $\delta$, i.e., the least integer $e$ such that $\delta$ is $R^{p^e}$-linear. In particular, we obtain a characterization of supersingular elliptic curves in terms of the level of the associated differential operator.Comment: 23 pages. Comments are welcom

On some local cohomology spectral sequences

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain applying a family of functors to a single module. For the second type we follow a completely different strategy as we start with the inverse system that we obtain by applying a covariant functor to an inverse system. The spectral sequences involve the right derived functors of the corresponding limit. We also have a version for contravariant functors. In all the introduced spectral sequences we provide sufficient conditions to ensure their degeneration at their second page. As a consequence we obtain some decomposition theorems that greatly generalize the well-known decomposition formula for local cohomology modules given by Hochster.Comment: 63 pages, comments are welcome. To appear in International Mathematics Research Notice

Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

The goal of this paper is twofold; on the one hand, motivated by questions raised by Schenzel, we explore situations where the Hartshorne--Lichtenbaum Vanishing Theorem for local cohomology fails, leading us to simpler expressions of certain local cohomology modules. As application, we give new expressions of the endomorphism ring of these modules. On the other hand, building upon previous work by \`Alvarez Montaner, we exhibit the shape of Lyubeznik tables of the so--called partially sequentially Cohen--Macaulay rings as introduced by Sbarra and Strazzanti.Comment: 13 pages, comments are welcom