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Search: All articles in the CJM digital archive with keyword cycles

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1. CJM 2014 (vol 67 pp. 639)

Gonzalez, Jose Luis; Karu, Kalle
 Projectivity in Algebraic Cobordism The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the same theory. Keywords:algebraic cobordism, quasiprojectivity, cobordism cyclesCategories:14C17, 14F43, 55N22

2. CJM 2014 (vol 67 pp. 198)

Murty, V. Kumar; Patankar, Vijay M.
 Tate Cycles on Abelian Varieties with Complex Multiplication We consider Tate cycles on an Abelian variety $A$ defined over a sufficiently large number field $K$ and having complex multiplication. We show that there is an effective bound $C = C(A,K)$ so that to check whether a given cohomology class is a Tate class on $A$, it suffices to check the action of Frobenius elements at primes $v$ of norm $\leq C$. We also show that for a set of primes $v$ of $K$ of density $1$, the space of Tate cycles on the special fibre $A_v$ of the NÃ©ron model of $A$ is isomorphic to the space of Tate cycles on $A$ itself. Keywords:Abelian varieties, complex multiplication, Tate cyclesCategories:11G10, 14K22

3. CJM 2013 (vol 66 pp. 505)

Arapura, Donu
 Hodge Theory of Cyclic Covers Branched over a Union of Hyperplanes Suppose that $Y$ is a cyclic cover of projective space branched over a hyperplane arrangement $D$, and that $U$ is the complement of the ramification locus in $Y$. The first theorem implies that the Beilinson-Hodge conjecture holds for $U$ if certain multiplicities of $D$ are coprime to the degree of the cover. For instance this applies when $D$ is reduced with normal crossings. The second theorem shows that when $D$ has normal crossings and the degree of the cover is a prime number, the generalized Hodge conjecture holds for any toroidal resolution of $Y$. The last section contains some partial extensions to more general nonabelian covers. Keywords:Hodge cycles, hyperplane arrangementsCategory:14C30

4. CJM 2013 (vol 65 pp. 1125)

Vandenbergen, Nicolas
 On the Global Structure of Special Cycles on Unitary Shimura Varieties In this paper, we study the reduced loci of special cycles on local models of the Shimura variety for $\operatorname{GU}(1,n-1)$. Those special cycles are defined by Kudla and Rapoport. We explicitly compute the irreducible components of the reduced locus of a single special cycle, as well as of an arbitrary intersection of special cycles, and their intersection behaviour in terms of Bruhat-Tits theory. Furthermore, as an application of our results, we prove the connectedness of arbitrary intersections of special cycles, as conjectured by Kudla and Rapoport. Keywords:Shimura varieties, local models, special cyclesCategory:14G35

5. CJM 2011 (vol 63 pp. 1345)

Jardine, J. F.
 Pointed Torsors This paper gives a characterization of homotopy fibres of inverse image maps on groupoids of torsors that are induced by geometric morphisms, in terms of both pointed torsors and pointed cocycles, suitably defined. Cocycle techniques are used to give a complete description of such fibres, when the underlying geometric morphism is the canonical stalk on the classifying topos of a profinite group $G$. If the torsors in question are defined with respect to a constant group $H$, then the path components of the fibre can be identified with the set of continuous maps from the profinite group $G$ to the group $H$. More generally, when $H$ is not constant, this set of path components is the set of continuous maps from a pro-object in sheaves of groupoids to $H$, which pro-object can be viewed as a Grothendieck fundamental groupoid". Keywords:pointed torsors, pointed cocycles, homotopy fibresCategories:18G50, 14F35, 55B30
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