A comparison theorem for l-adic cohomology

We show that, for certain types of rigid analytic varieties X and constructible l-adic sheaves (F_n)_n on, one has . As an application we obtain that, for an algebraic variety X and associated rigid analytic variety X^rig, the l-adic cohomology of X and X^rig agree.     

Every

It is known that congruence lattices of algebras in -permutable varieties satisfy non-trivial identities; however, the identities discovered so far are rather artificial and seem to have little intrinsic interest.

We show here that every -permutable variety satisfies the well-known and well-studied congruence identity . We also get a new condition equivalent to -permutability.

     

Harnack-Thom theorem for higher cycle groups and Picard varieties

We generalize the Harnack-Thom theorem to relate the ranks of the Lawson homology groups with -coefficients of a real quasiprojective variety with the ranks of its reduced real Lawson homology groups. In the case of zero-cycle group, we recover the classical Harnack-Thom theorem and generalize the classical version to include real quasiprojective varieties. We use Weil's construction of Picard varieties to construct reduced real Picard groups, and Milnor's construction of universal bundles to construct some weak models of classifying spaces of some cycle groups. These weak models are used to produce long exact sequences of homotopy groups which are the main tool in computing the homotopy groups of some cycle groups of divisors. We obtain some congruences involving the Picard number of a nonsingular real projective variety and the rank of its reduced real Lawson homology groups of divisors.

     

Ample vector bundles and Bordiga surfaces

Let X be a smooth complex projective variety and let Z ? X be a smooth surface, which is the zero locus of a section of an ample vector bundle ? of rank dimX – 2 ≥ 2 on X. Let H be an ample line bundle on X, whose restriction H _Z to Z is a very ample line bundle and assume that (Z, H _Z ) is a Bordiga surface, i.e., a rational surface having (?², ?? (4)) as its minimal adjunction theoretic reduction. Triplets (X, ?, H) as above are discussed and classified. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Quantum Cohomology Ring of Flag Varieties

We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263-277). We also give a geometric proof of the quantum Monk formula.

     

Balanced superprojective varieties

We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the geometry of superprojective spaces, we extend Donaldson’s definition of balanced manifolds to supermanifolds and we derive the new conditions of a balanced supermanifold. We apply the construction to superpoints viewed as submanifolds of superprojective spaces. We conclude with a list of open issues and interesting problems that can be addressed in the present context.     

导数FTIR结合统计学法应用于中药延胡索质量控制的研究

提出了用单次反射傅里叶变换红外光谱法直接测定延胡索及其伪品的新方法。采用OMNI采样器直接测定法测定了样品的红外光谱,并经过二阶导数光谱转换后进行峰位一致率检验。结果发现延胡索表皮以内部分和外表皮的二阶导数红外光谱峰位基本无差别,而且不同产地的道地药材具有较好的相关性。表皮以内部分于2050～650cm^-1区域在4cm^-1波长区域单位范围内进行统计学处理,结果延胡索与其伪品的差异性极其显。可以采用二阶导数FTIR结合统计学法直接、快速、准确地对延胡索与其伪品的表皮以内部分进行区别鉴定。     

利用傅里叶变换红外光谱法鉴定小麦品种

利用傅里叶变换红外(FTIR)光谱法分析了8个不同小麦品种根部的红外光谱图,对红外光谱图的吸收峰进行了归属分析,通过对各谱图的比对发现,在相同波数范围内,不同的小麦品种其红外谱图的形状、波数及吸收峰的多少有所不同。结果表明不同小麦品种的红外光谱图有明显的差异,其一在2800～2980cm-1波数范围内,此区反映的主要是甲基、亚甲基的伸缩振动,化合物分子链的长短、分子量的大小在此区有显现;其二差别较大的区域在1510～1730cm-1范围内,它反映的主要是酰胺的氮原子及α碳原子取代基的性质,可能是源于基因的差异,此区域内谱图差异较大。因此FTIR光谱法可用于不同小麦品种的鉴别。