Ana Jeremías López

Local homology and cohomology on schemes

Abstract We present a sheafified derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendiecks local duality theorem): for a quasi-compact separated scheme X and a “proregular” subscheme Z-for example, any separated noetherian scheme and any closed subscheme-there is a sort of adjointness between local cohomology supported in Z and left-derived completion along Z. In particular, left-derived completion can be identified with local homology, i.e., the homology of R H em•(RΛZ Q X−). Generalizations of a number of duality theorems scattered about the literature result: the Peskine-Szpiro duality sequence (generalizing local duality), the Warwick Duality theorem of Greenlees, the Affine Duality theorem of Hartshorne. Using Grothendieck Duality, we also get a generalization of a Formal Duality theorem of Hartshorne, and of a related local-global duality theorem. In a sequel we will develop the latter results further, to study Grothendieck duality and residues on formal schemes.

Localization in Categories of Complexes and Unbounded Resolutions

In this paper we show that for a Grothendieck category A and a complex E in C(A) there is an associated localization endofunctor l in D(A). This means that l is idempotent (in a natural way) and that the objects that go to 0 by l are those of the smallest localizing (= triangulated and stable for coproducts) subcategory of D(A) that contains E. As applications, we construct K-injective resolutions for complexes of objects of A and derive Brown representability for D(A) from the known result for D(R-mod), where R is a ring with unit. Received by the editors May 7, 1998; revised December 3, 1998. All three authors partially supported by Xunta de Galicia through research project XUGA20701A96 and Spain’s DGESIC grant PB97-0530. AMS subject classification: Primary: 18E30; secondary: 18E15, 18E35. c ©Canadian Mathematical Society 2000. 225

MECHANISMS OF THE EFFECTS OF EXOGENOUS LEVODOPA ON THE DOPAMINE-DENERVATED STRIATUM

The efficacy of exogenous levodopa (L-DOPA) is attributed to its conversion to dopamine by the enzyme aromatic L-amino-acid decarboxylase in striatal dopaminergic terminals. However, there is controversy about the mechanisms underlying the therapeutic and adverse effects of L-DOPA after almost all striatal dopaminergic afferents have disappeared (i.e. in the later stages of Parkinsons disease). After administration of 30mg/kg or 100mg/kg of L-DOPA, rats subjected to unilateral dopaminergic denervation showed intense contraversive rotation and a high density of Fos-immunoreactive nuclei throughout the denervated striatum, with no significant induction of Fos in the intact striatum. Injection of the central aromatic L-amino-acid decarboxylase inhibitor NSD-1015 30min before and 15min after the injection of L-DOPA suppressed the rotational behavior and the striatal induction of Fos. Comparison of results obtained in rats subjected to unilateral and bilateral dopaminergic denervation indicated that the presence of contralateral dopaminergic innervation does not significantly modulate the effects of L-DOPA on the denervated striatum. Serotonergic denervation led to slight and statistically non-significant decrease in the rotational behavior and Fos expression induced by high doses of L-DOPA (100mg/kg) in the dopamine-denervated striatum, but totally suppressed the rotational behavior and Fos expression induced by low doses of L-DOPA (30mg/kg). The present data indicate that the major effects observed after administration of exogenous L-DOPA are not due to a direct action of L-DOPA on dopamine receptors, or to extrastriatal release of dopamine, but to conversion of L-DOPA to dopamine by serotonergic terminals and probably some intrastriatal cells. Given that serotonergic neurons appear to play an important role in the action of L-DOPA in the later stages of Parkinsons disease, strategies targeting the serotonergic system should be considered for the treatment of Parkinsons disease and for combating undesirable side effects of L-DOPA therapy.

Construction of -structures and equivalences of derived categories

We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickards theorem on equivalence of bounded derived categories of modules. Also, we extend this result to bounded derived categories of quasi-coherent sheaves on separated divisorial schemes obtaining, in particular, Beiˇlinsons equivalences.

Depression and Cocaine Dependence

Presence of depression in cocaine-dependent users is relevant for treatment of these persons. This study assessed the presence of depressive symptomatology with a published Spanish translation of the Beck Depression Inventory for a sample of 115 Spanish cocaine-dependent users who were in outpatient treatment at Centers of Drug Dependence of Galicia, Spain. The mean score was 13.7 (SD=10.3), with 24.3% of the sample having scores which indicate clinical depression (cut off ≥ 21). These data underscore the need to assess the presence of depression in cocaine-dependent users who require treatment.

Studies in duality on noetherian formal schemes and non-noetherian ordinary schemes

Part 1: Duality and flat base change on formal schemes by L. Alonso, A. Jeremias, and J. Lipman Part 2: Greenlees-May duality on formal schemes by L. Alonso, A. Jeremias, and J. Lipman Part 3: Non-noetherian Grothendieck duality by J. Lipman Index.

Compactly generated t-structures on the derived category of a Noetherian ring

Abstract We study t -structures on D ( R ) the derived category of modules over a commutative Noetherian ring R generated by complexes in D fg − ( R ) . We prove that they are exactly the compactly generated t -structures on D ( R ) and describe them in terms of decreasing filtrations by supports of Spec ( R ) . A decreasing filtration by supports ϕ : Z → Spec ( R ) satisfies the weak Cousin condition if for any integer i , the set ϕ ( i ) contains all the immediate generalizations of each point in ϕ ( i + 1 ) . If a compactly generated t -structure on D ( R ) restricts to a t -structure on D fg ( R ) then the corresponding filtration satisfies the weak Cousin condition. If R has a pointwise dualizing complex the converse is true. If the ring R has dualizing complex then these are exactly all the t -structures on D fg b ( R ) .

Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes

This a first step to develop a theory of smooth, étale, and unramified morphisms between Noetherian formal schemes. Our main tool is the complete module of differentials, which is, a coherent sheaf whenever the map of formal schemes is of pseudofinite type. Among our results, we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitable closed subsets. We characterize unramifiedness by the vanishing of the module of differentials. Also we see that a smooth morphism of Noetherian formal schemes is flat and its module of differentials is locally free. The article closes with a version of Zariskis Jacobian criterion.

Spanish Adaptation of the NDSS (Nicotine Dependence Syndrome Scale) and Assessment of Nicotine-Dependent Individuals at Primary Care Health Centers in Spain

The availability of adequate instruments for the assessment of nicotine dependence is an important factor that is relevant in the area of tobacco addiction. In this study, we present a Spanish validation of the Nicotine Dependence Syndrome Scale (NDSS) (Shiffman, Waters, & Hickcox, 2004). The sample was composed ofpatients, all daily smokers, who visited their General Practitioner (GP) at five Primary Health Care Centers in different cities of Spain (N = 637). The results indicated adequate reliability for the general factor that assesses nicotine dependence (NDSS-Total) (Cronbachs alpha = .76). Factor analysis confirms the five factors of the original validation: Drive, Continuity, Stereotypy, Priority, and Tolerance. It must be noted that reliability is adequate for the first, and moderate or low for the rest. The NDSS-T and its scales correlate significantly with the Fagerström Test for Nicotine Dependence (FTND), with the nicotine dependence criteria of the Diagnostic and Statistical Manual of Mental Disorders IV (DSM-IV) as assessed through the Structured Clinical Interview for DSM-IV (SCID), with carbon monoxide levels in expired air (CO), and with the number of cigarettes smoked. The ROC curve indicates that the NDSS-T has a score of .79 which is under the curve (.69 for the FTND), thus the prediction of nicotine dependence is adequate. We conclude that this instrument is useful (in terms of its total score NDSS-T) for assessing nicotine dependence for Spanish smokers (in Spain), as has been found in other countries, language groups, and cultures.

Fluorination Effects on NOS Inhibitory Activity of Pyrazoles Related to Curcumin

A series of new (E)-3(5)-[β-(aryl)-ethenyl]-5(3)-phenyl-1H-pyrazoles bearing fluorine atoms at different positions of the aryl group have been synthesized starting from the corresponding β-diketones. All compounds have been characterized by elemental analysis, DSC as well as NMR (1H, 13C, 19F and 15N) spectroscopy in solution and in solid state. Three structures have been solved by X-ray diffraction analysis, confirming the tautomeric forms detected by solid state NMR. The in vitro study of their inhibitory potency and selectivity on the activity of nNOS and eNOS (calcium-calmodulin dependent) as well as iNOS (calcium-calmodulin independent) isoenzymes is presented. A qualitative structure–activity analysis allowed the establishment of a correlation between the presence/absence of different substituents with the inhibition data proving that fluorine groups enhance the biological activity. (E)-3(5)-[β-(3-Fluoro-4-hydroxyphenyl)-ethenyl]-5(3)-phenyl-1H-pyrazole (13), is the best inhibitor of iNOS, being also more selective towards the other two isoforms.