Complex varieties for which the Chow group mod $n$ is not finite

2002 ◽  
Vol 11 (1) ◽  
pp. 41-100 ◽  
Author(s):  
Chad Schoen
Keyword(s):  
Chow Group ◽  
Complex Varieties

scholarly journals Strong submeasures and applications to non-compact dynamical systems

2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG
Keyword(s):  
Metric Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Compact Metric Space ◽  
Basic Properties ◽  
Banach Theorem ◽  
Complex Varieties ◽  
Definition Of ◽  
Meromorphic Maps

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.

scholarly journals ON THE CHOW RING OF CERTAIN LEHN–LEHN–SORGER–VAN STRATEN EIGHTFOLDS

2021 ◽  
pp. 1-24
Author(s):  
CHIARA CAMERE ◽  
ALBERTO CATTANEO ◽  
ROBERT LATERVEER
Keyword(s):  
Chow Group ◽  
Chow Ring ◽  
Similar Statement ◽  
Intersection Product ◽  
Finite Dimensional

Abstract We consider a 10-dimensional family of Lehn–Lehn–Sorger–van Straten hyperkähler eightfolds, which have a non-symplectic automorphism of order 3. Using the theory of finite-dimensional motives, we show that the action of this automorphism on the Chow group of 0-cycles is as predicted by the Bloch–Beilinson conjectures. We prove a similar statement for the anti-symplectic involution on varieties in this family. This has interesting consequences for the intersection product of the Chow ring of these varieties.

scholarly journals Electroacupuncture Reduces Weight in Diet-Induced Obese Rats via Hypothalamic Tsc1 Promoter Demethylation and Inhibition of the Activity of mTORC1 Signaling Pathway

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Jincheng Leng ◽  
Feng Xiong ◽  
Junpeng Yao ◽  
Xiahuan Dai ◽  
Yulei Luo ◽  
...  
Keyword(s):  
Signaling Pathway ◽  
Body Fat ◽  
Mammalian Target Of Rapamycin ◽  
Gene Promoter ◽  
Chow Group ◽  
Diet Group ◽  
The Body ◽  
Sprague Dawley ◽  
Tsc1 Gene ◽  
Mtorc1 Signaling

Subject. The study aimed to investigate the mechanism of electroacupuncture reducing weight via tuberous sclerosis complex 1 (Tsc1) promoter methylation, inhibiting the mammalian target of rapamycin complex 1 (mTORC1) pathway. Materials and Methods. Male Sprague-Dawley rats were divided into chow-fed group (chow group) or high-fat diet group (HF group) for 14 weeks. The obesity rats in HF group were randomly divided into electroacupuncture group (EA group) and diet-induced obesity (DIO) group, which received EA stimulation on bilateral ST25, RN12, SP6, and ST36 for 4 weeks or no further treatment, respectively. Methylation of the Tsc1 gene promoter and expression of agouti-related protein (AgRP), neuropeptide Y (NPY), and proopiomelanocortin (PoMC) were detected at the 18th week. Results. At week 18, weight, body fat, and the body fat rate in DIO group were significantly higher than those of the chow and EA group. Compared with the chow group, the DIO group had increased methylation of the Tsc1 gene promoter and expression of mTORC1, AgRP, and NPY gene and decreased PoMC in the hypothalamus; after EA, methylation of the Tsc1 gene promoter, mRNA, and protein of the mTORC1 and expression of AgRP and NPY gene decreased and PoMC increased significantly. Conclusions. Our study could shed light on the potential pathway where EA exerts effects on the mechanism of EA treatment for obesity through the hypothalamic Tsc1 promoter demethylation and inhibition of the activity of mTORC1 signaling pathway.

scholarly journals Beilinson's Hodge Conjecture for Smooth Varieties

2013 ◽  
Vol 11 (2) ◽  
pp. 243-282 ◽  
Author(s):  
Rob de Jeu ◽  
James D. Lewis
Keyword(s):  
Projective Variety ◽  
Chow Group ◽  
Hodge Conjecture ◽  
Generic Point ◽  
Higher Chow Group ◽  
Cycle Class

AbstractLet U/ℂ be a smooth quasi-projective variety of dimension d, CHr (U,m) Bloch's higher Chow group, andclr,m: CHr (U,m) ⊗ ℚ → homMHS (ℚ(0), H2r−m (U, ℚ(r)))the cycle class map. Beilinson once conjectured clr,m to be surjective [Be]; however, Jannsen was the first to find a counterexample in the case m = 1 [Ja1]. In this paper we study the image of clr,m in more detail (as well as at the “generic point” of U) in terms of kernels of Abel-Jacobi mappings. When r = m, we deduce from the Bloch-Kato conjecture (now a theorem) various results, in particular that the cokernel of clm,m at the generic point is the same for integral or rational coefficients.

scholarly journals Troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique sur un corps de fonctions d'une variable

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Jean-Louis Colliot-Thélène ◽  
Alena Pirutka
Keyword(s):  
Function Field ◽  
Cohomology Group ◽  
Chow Group ◽  
Hodge Conjecture ◽  
Complex Curve ◽  
The Third ◽  
Generic Fibre ◽  
Nous Montrons ◽  
Unramified Cohomology ◽  
Cubic Threefold

En combinant une m\'ethode de C. Voisin avec la descente galoisienne sur le groupe de Chow en codimension $2$, nous montrons que le troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique lisse d\'efini sur le corps des fonctions d'une courbe complexe est nul. Ceci implique que la conjecture de Hodge enti\`ere pour les classes de degr\'e 4 vaut pour les vari\'et\'es projectives et lisses de dimension 4 fibr\'ees en solides cubiques au-dessus d'une courbe, sans restriction sur les fibres singuli\`eres. --------------- We prove that the third unramified cohomology group of a smooth cubic threefold over the function field of a complex curve vanishes. For this, we combine a method of C. Voisin with Galois descent on the codimension $2$ Chow group. As a corollary, we show that the integral Hodge conjecture holds for degree $4$ classes on smooth projective fourfolds equipped with a fibration over a curve, the generic fibre of which is a smooth cubic threefold, with arbitrary singularities on the special fibres. Comment: in French

scholarly journals Comparing K -theories for complex varieties

2001 ◽  
Vol 123 (5) ◽  
pp. 779-810 ◽  
Author(s):  
Eric M. Friedlander ◽  
Mark E. Walker
Keyword(s):  
Complex Varieties

scholarly journals On two arithmetic theta lifts

2018 ◽  
Vol 154 (10) ◽  
pp. 2090-2149 ◽  
Author(s):  
Stephan Ehlen ◽  
Siddarth Sankaran
Keyword(s):  
Modular Forms ◽  
Theta Functions ◽  
Chow Group ◽  
Shimura Varieties ◽  
Green Functions ◽  
Theta Lift ◽  
Moderate Growth ◽  
Generating Series ◽  
Cm Points ◽  
The Difference

Our aim is to clarify the relationship between Kudla’s and Bruinier’s Green functions attached to special cycles on Shimura varieties of orthogonal and unitary type, which play a key role in the arithmetic geometry of these cycles in the context of Kudla’s program. In particular, we show that the generating series obtained by taking the differences of the two families of Green functions is a non-holomorphic modular form and has trivial (cuspidal) holomorphic projection. Along the way, we construct a section of the Maaß lowering operator for moderate growth forms valued in the Weil representation using a regularized theta lift, which may be of independent interest, as it in particular has applications to mock modular forms. We also consider arithmetic-geometric applications to integral models of $U(n,1)$ Shimura varieties. Each family of Green functions gives rise to a formal arithmetic theta function, valued in an arithmetic Chow group, that is conjectured to be modular; our main result is the modularity of the difference of the two arithmetic theta functions. Finally, we relate the arithmetic heights of the special cycles to special derivatives of Eisenstein series, as predicted by Kudla’s conjecture, and describe a refinement of a theorem of Bruinier, Howard and Yang on arithmetic intersections against CM points.

scholarly journals Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles

2007 ◽  
Vol 1 (2) ◽  
pp. 163-181 ◽  
Author(s):  
Masanori Asakura ◽  
Shuji Saito
Keyword(s):  
Chow Group
Sign in / Sign up

Export Citation Format

Share Document