Related papers: On the image of higher signature maps

Let $(X,o)$ be a complex normal surface singularity with rational homology sphere link and let $\widetilde{X}$ be one of its good resolutions. Fix an effective cycle $Z$ supported on the exceptional curve and also a possible Chern class…

Let $(X,o)$ be a complex normal surface singularity. We fix one of its good resolutions $\widetilde{X}\to X$, an effective cycle $Z$ supported on the reduced exceptional curve, and any possible (first Chern) class $l'\in…

The classical cycle class map for a smooth complex variety sends cycles in the Chow ring to cycles in the singular cohomology ring. We study two cycle class maps for smooth real varieties: the map from the I-cohomology ring to singular…

We investigate the surjectivity of the real cycle class map from $I$-cohomology to classical intergral cohomology for some real smooth varieties, in particular surfaces. This might be considered as one of several possible incarnations of…

We present a version of projective bundle theorem in MW-motives (resp. Chow-Witt rings), which says that $\widetilde{CH}^*(\mathbb{P}(E))$ is determined by $\widetilde{CH}^*(X)$, $\widetilde{CH}^*(X,det(E)^{\vee})$, $CH^*(X)$ and $Sq^2$ for…

In this paper, we study equivariant real cycle class maps for group actions on real schemes, with a view toward Witt-sheaf characteristic classes. The cycle class maps take values in singular cohomology of the real points of the quotient…

Let $\bar{X}$ be a smooth quasi-projective $d$-dimensional variety over a field $k$ and let $D$ be an effective Cartier divisor on it. In this note, we construct cycle class maps from (a variant of) the higher Chow group with modulus of the…

Consider the cycle class map cl_{r,m} : CH^r(U,m;\Q) \to \Gamma H^{2r-m}(U,\Q(r)), where CH^r(U,m;\Q) is Bloch's higher Chow group (tensored with \Q) of a smooth complex quasi-projective variety U, and H^{2r-m}(U,\Q(r)) is singular…

We study the Chow group of zero-cycles of smooth projective varieties over local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with…

Let $k$ be a field and $V$ an $k$-vector space. For a family $\bar P=\{ P_i\}_{1\leq i\leq c}, $ of polynomials on $V$, we denote by $\mathbb X _{\bar P}\subset V$ the subscheme defined by the ideal generated by $ \bar P$. We show the…

We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen--Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological…

Let $(V,q)$ be a non-degenerate $n$-dimensional quadratic space over the rationals of real signature $(r,s)$. For every integer $1\leq k \leq \min\{r,n-2\}$ we construct classes in the cohomology of arithmetic subgroups of $\mathrm{O}(V)$…

We explicitly describe cycle-class maps c_H from motivic cohomology to absolute Hodge cohomology, for smooth quasi-projective and (some) proper singular varieties, and compute special cases of the latter. For smooth projective varieties, we…

We study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding to two distinct universality classes with respective central…

In \cite{Broer1993}, it was shown that certain line bundles on $\widetilde{\mathcal{N}}=T^*G/B$ have vanishing higher cohomology. We prove a generalization of this theorem for real reductive algebraic groups. More specifically, if…

A conjecture of Colliot-Th\'{e}l\`{e}ne predicts that for a smooth projective variety $X$ over a finite extension $k$ of $\mathbb{Q}_p$ the kernel of the Albanese map $\text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k)$ is the direct sum of a…

Let X be a separated scheme of finite type over a field k and D a non-reduced effective Cartier divisor on it. We attach to the pair (X, D) a cycle complex with modulus, whose homotopy groups - called higher Chow groups with modulus -…

We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under…

The real cycle class map $H^i(X,\underline{I}^j(\mathcal{L})) \rightarrow H^i_\text{sing}(X(\mathbb{R}),\mathbb{Z}(\mathcal{L}))$ is an isomorphism for $j\geq \dim(X)+1$ for any scheme $X$ over $\mathbb{R}$ by a result of Jacobson. It is…

A main theme of the paper is a conjecture of Bloch-Kato on the image of $p$-adic regulator maps for a proper smooth variety $X$ over an algebraic number field $k$. The conjecture for a regulator map of particular degree and weight is…