On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules

Let $(R,\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\ge}-1$ be an integer and r=\depth_k(I,N) the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536). For a subset S\subseteq \Spec R we set S_{{\ge}k}={\p\in S\mid\dim(R/\p){\ge}k}. We first prove in this paper that \Ass_R(H^j_I(N))_{\ge k} is a finite set for all $j{\le}r$}. Let \fN=\oplus_{n\ge 0}N_n be a finitely generated graded \fR-module, where \fR is a finitely generated standard graded algebra over $R_0=R$. Let $r$ be the eventual value of \depth_k(I,N_n). Then our second result says that for all $l{\le}r$ the sets \bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k} are stable for large $n$.Comment: To appear in Communication in Algebr

On the cofiniteness of generalized local cohomology modules

Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$ and $M$, $N$ two finitely generated $R$-modules. The aim of this paper is to investigate the $I$-cofiniteness of generalized local cohomology modules \displaystyle H^j_I(M,N)=\dlim\Ext^j_R(M/I^nM,N) of $M$ and $N$ with respect to $I$. We first prove that if $I$ is a principal ideal then $H^j_I(M,N)$ is $I$-cofinite for all $M, N$ and all $j$. Secondly, let $t$ be a non-negative integer such that \dim\Supp(H^j_I(M,N))\le 1 \text{for all} j Then $H^j_I(M,N)$ is $I$-cofinite for all $j<t$ and \Hom(R/I,H^t_I(M,N)) is finitely generated. Finally, we show that if $\dim(M)\le 2$ or $\dim(N)\le 2$ then $H^j_I(M,N)$ is $I$-cofinite for all $j$.Comment: 16 page

Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas obtained unify several known results and allow us to characterize the differentiability of the infimal convolution which plays an important role in variational analysis and optimization

Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure

We prove the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents and elastic labor supply. The method of proof relies on exploiting the existence of Lagrange multipliers in infinite dimensional spaces and the link between Pareto-optima and competitive equilibria.Optimal growth model, Lagrange multipliers, single-sector growth model, competitive equilibrium, elastic labor supply.

No-arbitrage condition and existence of equilibrium with dividends

In this paper we first give an elementary proof of existence of equilibrium with dividends in an economy with possibly satiated consumers.We then introduce a no-arbitrage condition and show that it is equivalent to the existence of equilibrium with dividends.equilibrium with dividends, economy with possibly satiated consumers, no-arbitrage condition

Endogenous Fiscal Policies, Environmental Quality, and Status-Seeking Behavior.

This paper analyzes endogenous fiscal policy and public decision in an endogenous growth model where agents care about social status and environmental quality. The quest for a higher status is assimilated to a preference for capital wealth. The government uses income tax to finance infrastructure and environmental protection, and maximizes individual welfare. We find that accounting for preferences for social status and environmental quality may lead to an allocation of tax revenue in favor of cleanup effort to the detriment of infrastructure. It does not necessary have a negative impact on growth. Status seeking can however harm economic growth and environmental quality when its motive is important enough. Finally, we show that economic growth is consistent with environmental preservation but is not necessarily welfare-improving as in the case of absence of status-seeking behavior.Endogenous policy; endogenous growth; environmental quality; status-seeking; public expenditure; Wagner's law.