Remarks on Murre's conjecture on Chow groups

Xu, Ke; Ze, XU

doi:10.1017/is013005020jkt228

Cited by 8 publications

(7 citation statements)

References 18 publications

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“…Proposition 2.8 shows that Murre's conjecture (B) for motives of abelian type implies Murre's conjecture (C) for motives of abelian type. Finally, that Murre's conjecture (D) for motives of abelian type implies Murre's conjecture (B) for motives of abelian type relies on the main theorem of K. Xu and Z. Xu [23] which we reproduce as Theorem 2.6. A combination of Theorems 2.9 and Remark 2.10 is the following.…”

Section: Introductionmentioning

confidence: 82%

Remarks on motives of abelian type

Vial¹

2017

Tohoku Math. J. (2)

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A motive over a field k is of abelian type if it belongs to the thick and rigid subcategory of Chow motives spanned by the motives of abelian varieties over k. This paper contains three sections of independent interest. First, we show that a motive which becomes of abelian type after a base field extension of algebraically closed fields is of abelian type. Given a field extension K/k and a motive M over k, we also show that M is finitedimensional if and only if M K is finite-dimensional. As a corollary, we obtain Chow-Künneth decompositions for varieties that become isomorphic to an abelian variety after some field extension. Second, let Ω be a universal domain containing k. We show that Murre's conjectures for motives of abelian type over k reduce to Murre's conjecture (D) for products of curves over Ω. In particular, we show that Murre's conjecture (D) for products of curves over Ω implies Beauville's vanishing conjecture on abelian varieties over k. Finally, we give criteria on Chow groups for a motive to be of abelian type. For instance, we show that M is of abelian type if and only if the total Chow group of algebraically trivial cycles CH * (M Ω ) alg is spanned, via the action of correspondences, by the Chow groups of products of curves. We also show that a morphism of motives f : N → M , with N finitedimensional, which induces a surjection f * : CH * (N Ω ) alg → CH * (M Ω ) alg also induces a surjection f * : CH * (N Ω ) hom → CH * (M Ω ) hom on homologically trivial cycles.

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Section: Introductionmentioning

confidence: 82%

Remarks on motives of abelian type

Vial¹

2017

Tohoku Math. J. (2)

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“…In contradiction, however, several groups have demonstrated improved SNR of OCT by using different optical amplifiers, such as semiconductor amplifiers and fiber amplifiers based on stimulated emission and stimulated Raman scattering, respectively. SNR improvements on the order of 10 to 20 dB [24,[41][42][43], extended depth, and improved contrast in OCT imaging, have been reported when optical amplifiers are used.…”

Section: Discussionmentioning

confidence: 99%

Enhancement of optical coherence microscopy in turbid media by an optical parametric amplifier

Zhao

Liu

et al. 2014

J. Biophoton

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We report the enhancement in imaging performance of a spectral-domain optical coherence microscope (OCM) in turbid media by incorporating an optical parametric amplifier (OPA). The OPA provides a high level of optical gain to the sample arm, thereby improving the signal-to-noise ratio of the OCM by a factor of up to 15 dB. A unique nonlinear confocal gate is automatically formed in the OPA, which enables selective amplification of singly scattered (ballistic) photons against the multiply-scattered light background. Simultaneous enhancement in both imaging depth and spatial resolution in imaging microstructures in highly light-scattering media are demonstrated with the combined OPA-OCM setup. Typical OCM inteferograms (left) and images (right) without and with OPA.

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“…Recently a few researchers are moving to digital prediction, the numerical method is being used to analyze the static and dynamic properties of 3D braided composite. In order to avoid the time consuming and costly experiments, usually the unit cell based model was used to predict the stiffness and strength . Zhang et al studied the homogenization of 3D braided composite based on the unit cell geometry model .…”

Section: Introductionmentioning

confidence: 99%

“…Zhang et al studied the homogenization of 3D braided composite based on the unit cell geometry model . Xu studied the failure behavior of meso‐scale unit cell of 3D braided composite. Considering the importance of notch test as a measure of the damage tolerance characteristics of structural composites, this paper studies the influence of fiber architecture on the notch strength of 3D braided composites under tensile and compressive loading.…”

Section: Introductionmentioning

confidence: 99%

Open hole tension and compression behavior of 3D braided composites

et al. 2020

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The damage tolerant behavior of 3D braided composites is evaluated in terms of the open‐hole notch strength test under tensile and compressive loading. The influence of fiber architecture is evaluated by comparing 3D braid with and without axial yarns as well as laminated composites based on ASTM quasi‐static tension and compression testing standard. The results show that the notched and un‐notched properties of the two types of 3D braided composites are similar under tension and compression loading. Comparing to laminates, both types of 3D braided composites demonstrated superior notch insensitivity than laminated composites. For the failure behavior of the 3D braided composites, under tension loading, crack of both notched specimens tends to propagate along the notch and finally render the specimen to failure. Clear cracks usually presented on the samples without axial yarns, while not for the specimens with axial yarn. Under compression loading, the two types of 3D braided composite are also macroscopically similar, showing transverse fracture. The modified Fabric Geometry Model is used to predict the tensile properties of 3D braided composite. The predicted and experimental results are shown to be in good agreement.

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Remarks on Murre's conjecture on Chow groups

Cited by 8 publications

References 18 publications

Remarks on motives of abelian type

Remarks on motives of abelian type

Enhancement of optical coherence microscopy in turbid media by an optical parametric amplifier

Open hole tension and compression behavior of 3D braided composites

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