Linear Koszul duality Mirković, Ivan; Riche, Simon
Compositio mathematica,
01/2010, Letnik:
146, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper we construct, for F1 and F2 subbundles of a vector bundle E, a ‘Koszul duality’ equivalence between derived categories of m-equivariant coherent(dg-)sheaves on the derived intersection ...$F_1 \rcap _E F_2$, and the corresponding derived intersection $F_1^{\perp } \rcap _{E^*} F_2^{\perp }$. We also propose applications to Hecke algebras.
In this paper we prove that the linear Koszul duality isomorphism for convolution algebras in K-homology defined in a previous paper and the Fourier transform isomorphism for convolution algebras in ...Borel-Moore homology are related by the Chern character. So, Koszul duality appears as a categorical upgrade of Fourier transform of constructible sheaves. This result explains the connection between the categorification of the Iwahori-Matsumoto involution for graded affine Hecke algebras (due to Evens and the first author) and for usual affine Hecke algebras (obtained in a previous paper).
We focused on the relationship of 0.5% tetracaine- and 0.4% oxybuprocaine-induced corneal anesthesia in rats, and pentadecapeptide BPC 157 (0.4 µg/eye), along with nitric oxide synthase (NOS) ...inhibitor N(gamma)-nitro-L-arginine methyl ester (L-NAME) (0.1 mg/eye) and/or NOS substrate L-arginine (2 mg/eye), applied in the form of eye drops. We assessed corneal sensitivity recovery (Cochet-Bonnet esthesiometer), corneal lesion elimination (staining with 10% fluorescein) and decrease in tear volume (Schirmer test). BPC 157 administration had a full counteracting effect. Recovery also occurred in the presence of NOS blockade and NOS substrate application. L-arginine eventually shortened duration of corneal insensitivity and exerted corneal lesion counteraction (and counteraction of tetracaine-induced decrease of tear volume) only in earlier but not in later period. L-NAME application led to longer duration of corneal insensitivity, increase in corneal lesions and decrease in tear volume. When L-NAME and L-arginine were applied together, they antagonized each other’s effect. These distinctions may indicate particular NOS involvement (corneal insensitivity
vs
. corneal lesion along with tear production), distinctively affected by the administration of NO agents. However, additional BPC 157 co-administration would re-establish counteraction over topical ophthalmic anesthetic-induced effect, be it in its early or late course. We suggest BPC 157 as an antidote to topical ophthalmic anesthetics.
We show that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central ...character are the same as coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber. The first step is to observe that the derived functor of global sections provides an equivalence between the derived category of D-modules (with no divided powers) on the flag variety and the appropriate derived category of modules over the corresponding Lie algebra. Thus the "derived" version of the Beilinson-Bernstein localization theorem holds in sufficiently large positive characteristic. Next, one finds that for any smooth variety this algebra of differential operators is an Azumaya algebra on the cotangent bundle. In the case of the flag variety it splits on Springer fibers, and this allows us to pass from P-modules to coherent sheaves. The argument also generalizes to twisted D-modules. As an application we prove Lusztig's conjecture on the number of irreducible modules with a fixed central character. We also give a formula for behavior of dimension of a module under translation functors and reprove the Kac-Weisfeiler conjecture. The sequel to this paper BMR2 treats singular infinitesimal characters.
We use linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras studied in previous papers of the authors, to give a geometric ...realization of the Iwahori--Matsumoto involution of affine Hecke algebras. More generally we prove that linear Koszul duality is compatible with convolution in a general context related to convolution algebras.
In this paper we continue the study (initiated in a previous article of the authors) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior ...algebras. We construct this duality in a very general setting, and prove its compatibility with morphisms of vector bundles and base change.
We report an ongoing attempt to establish in algebraic geometry certain analogues of topological ideas, The main goal is to associate to a scheme X over a commutative ring k its “relative motivic ...homology” which is again an algebro geometric object over the base k. This is motivated by Number Theory, so the Poincaré duality for this relative motivic homology should be an algebro geometric incarnation of Class Field Theory.
Usprkos tomu što je mehanička ventilacija jedan od osnovnih postupaka spašavanja života u jedinicama intenzivne medicine, danas je nakon mnogih provedenih istraživanja jasno da pogrešno primijenjena ...mehanička ventilacija može napraviti značajnu štetu na ranije zdravim plućima ili pogoršati ozljedu bolesnih pluća te se u modernom pristupu ventilaciji maksimalno individualizira pristup, odnosno mehaničku ventilacija se individualno
prilagođava stanju pluća pojedinog bolesnika. Usprkos tomu što postoje znanstveno dokazane metode smanjenja plućne ozljede, studije su pokazale da se u praksi kod velikog broja bolesnika one ne primjenjuju, odnosno ne mjere se parametri bitni za njihovo određivanje. Za individualizaciju ventilacije od intubacije do ekstubacije potrebno je nekoliko elementarnih alata kod kojih nam može pomoći umjetna inteligencija. To su incijalna optimizacija pozitivnog tlaka na kraju ekspirija, evaluacija i primjena manevara ponovog otvaranja kolabiranih dijelova pluća (engl. lung recruitment maneuver – RM), primjena moda ventilacije koji se može od udaha do udaha adaptirati na stanje bolesnikovih pluća, optimizacija plinova u krvi, optimizacija sinkronizacije bolesnika i ventilatora automatskim praćenjem krivulja mehaničke ventilacije te u konačnici alat za kvalitetnu procjenu sposobnosti
bolesnika za odvajanje i samostalno disanje uz analizu potencijalnih problema kod odvajanja i njihove korekcije. To je moguće postići kombinacijom više alata, kao što su npr. alat tlak-volumen (engl. pressure – volume tool – PV-tool) uz ezofagealno mjerenje tlaka, adaptivna suportivna ventilacija (ASV) + Intellivent-ASV kao mod disanja, Intellisync+ te alat za olakšano odvajanje od respiratora (engl. quick weaning tool QuickWean) i test spontanog disanja (engl. spontaneous breathing trial – SBT) dostupni na uređajima za mehaničku ventilaciju. Kombinacijom ovih alata moguće je inicijalno optimizirati mehaničku ventilaciju, a zahvaljujući automatiziranoj pametnoj tehnologiji i individualizirati praktički svaki udah bolesnika te na minimum smanjiti vrijeme potrebno za pripremu odvajanja bolesnika od mehaničke ventilacije te ekstubaciju, a u konačnici i smanjiti smrtnost bolesnika
na mehaničkoj ventilaciji.
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