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Ragnar-Olaf Buchweitz 《Advances in Mathematics》2008,217(1):205-242
We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so-called (derived) Hochschild complex of a morphism; the Hochschild cohomology and homology groups are then the Ext and Tor groups of that complex. We prove that these objects are well defined, extend the known cases, and have the expected functorial and homological properties such as graded commutativity of Hochschild cohomology and existence of the characteristic homomorphism from Hochschild cohomology to the (graded) centre of the derived category. 相似文献
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Cramer N Buchweitz M Laschat S Frey W Baro A Mathieu D Richter C Schwalbe H 《Chemistry (Weinheim an der Bergstrasse, Germany)》2006,12(9):2488-2503
Cylindramide (1) was built up from three components: a hydroxyornithine derivative 7, a tetrazolylsulfone 8, and a substituted pentalene subunit 9. Derivative 7 was prepared in a six-step reaction sequence involving the Wittig reaction and a Sharpless asymmetric dihydroxylation starting from N-Boc-3-aminopropanal (12). Tetrazolylsulfone 8 was accessible in four steps from dioxinone 22. The synthesis of the pentalene fragment 9 started from cycloocta-1,5-diene 26, that was converted into enantiopure bicyclo[3.3.0]octanedione 29. The latter was functionalized to give derivative 9. The total synthesis was accomplished by inducing C-C bond formation by Sonogashira coupling of derivatives 9 and 7 followed by olefination with tetrazolylsulfone 8 under Julia-Kocienski conditions, macrocyclization, and subsequent Lacey-Dieckmann condensation to form the tetramic acid unit. As indicated by extensive 1H and 13C NMR spectroscopic investigations (DQF-COSY, ROESY spectra), the stereochemistry of synthetic cylindramide (1) corresponds with that of the naturally occurring product. ROE data were used for molecular modeling of the lowest-energy structures for cylindramide. 相似文献
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Maria Buchweitz Gennadi Gudi Reinhold Carle Dietmar R. Kammerer Hartwig Schulz 《Journal of Raman spectroscopy : JRS》2012,43(12):2001-2007
The FT‐Raman spectra of the chloride salts of pelargonidin‐3‐glucoside, cyanidin‐3‐glucoside and delphinidin‐3‐glucoside, their structures at pH 5.0 and their interaction with aluminium and ferric ions are presented for the first time and discussed with regard to their spectroscopic response. Two marker bands at approximately 1510 and 1330/1350 cm−1 and one band at approximately 1330/1350 cm−1 were identified being characteristic for the formation of ferric and aluminium chelates, respectively, of cyanidin‐3‐glucoside and delphinidin‐3‐glucoside. In contrast, pelargonidin‐3‐glucoside, exhibiting one single hydroxyl group in the B‐ring, did not form metal chelates, which could be clearly demonstrated by missing marker bands. The formation of anthocyanin–metal chelates was also verified in model systems containing commercial sugar beet pectin and a pectic polysaccharide fraction isolated thereof, respectively. In addition, the absence of anthocyanin–metal chelates in systems prepared with citrate buffer was confirmed, and the effects of low and high methoxylated citrus pectins on chelate formation were studied. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Luchezar L. Avramov Ragnar-Olaf Buchweitz Srikanth Iyengar 《Inventiones Mathematicae》2007,169(1):1-35
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules
over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class – a substitute
for the length of a free complex – and on the rank of a differential module in terms of invariants of its homology. These
results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization
of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes
over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings. 相似文献
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In this paper, we outline the construction of obstructions tok-formality wherek is a field of arbitrary characteristic. We show that the obstructions to intrinsick-formality of a graded algebraH
* lie in the Hochschild cohomologyH H
m,1
(H
*/k, H
*). We calculate explicitly the Hochschild cohomology of the algebraH(ℂP
∞/ℂP
n
;k) and deduce that the stunted complex projective space ℂP
∞/ℂP
n
is intrinsicallyk-formal for any fieldk.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
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