Related papers: Zero-cycles on self-product of modular curves

Let X be a smooth projective variety. Starting with a finite set of cycles on powers X^m of X, we consider the Q-vector subspaces of the Q-linear Chow groups of the X^m obtained by iterating the algebraic operations and pullback and push…

Let G be a finite abelian group. We will consider a skew product extension of a product of two Cantor minimal Z-systems associated with a G-valued cocycle. When G is non-cyclic and the cocycle is non-degenerate, it will be shown that the…

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

In this paper we prove that the cohomology groups with compact support of stacks of shtukas are modules of finite type over a Hecke algebra. As an application, we extend the construction of excursion operators, defined by V. Lafforgue on…

Based on the combinatorial description of the moduli spaces of curves provided by Strebel differentials, Witten and Kontsevich have introduced combinatorial cohomology classes $W_{(m_0,m_1,m_2,\dots),n}$, and conjectured that these can be…

We show how to make the additive Chow groups of Bloch-Esnault, Ruelling and Park into a graded module for Bloch's higher Chow groups, in the case of a smooth projective variety over a field. This yields a a projective bundle formula as well…

Rost defined the Chow group of algebraic cycles with coefficients in a locally constant torsion etale sheaf. We generalize the definition to allow non-torsion coefficients. Chow groups with twisted coefficients are related to Serre's notion…

It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we construct nontrivial homomorphisms from infinite-genus mapping…

Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X, all having a common point, such that every effective one-cycle on X is rationally…

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell-Jones conjecture…

Let $X$ be a smooth projective variety over a field of characteristic $0$ and $L$ an ample divisor. In this paper we study the Weak Lefschetz conjecture for Chow groups using the technique employed by Grothendieck in his study of the…

We identify Cech cocycles in nonabelian (formal) group cohomology with Maurer-Cartan elements in a suitable L-infinity algebra. Applications to deformation theory are described.

We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…

We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the…

Let $E$ be the Fermat cubic curve over $\bar{\mathbb{Q}}$. In 2002, Schoen proved that the group $CH^2(E^3)/\ell$ is infinite for all primes $\ell\equiv 1\pmod 3$. We show that $CH^2(E^3)/\ell$ is infinite for all prime numbers $\ell> 5$.…

We prove excision in entire and periodic cyclic cohomology and construct a Chern-Connes character for Fredholm modules over a C*-algebra without summability restrictions, taking values in a variant of Connes's entire cyclic cohomology.…

Ceci est un rapport sur l'article "A finiteness theorem for zero-cycles over p-adic fields" (arXiv:math/0605165) de Shuji Saito et Kanetomo Sato. ----- This is a survey on the paper "A finiteness theorem for zero-cycles over p-adic fields"…

In this note, we establish isomorphisms up to bounded torsion between relative $K_0$-groups and Chow groups with modulus as defined by Binda-Saito.

We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by…

We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to construct finitely generated torsion-free groups that have only finitely many classes of conjugate…