Related papers: On rational quadratic cocycles

The automorphic cohomology of a connected reductive algebraic group defined over Q decomposes as a direct algebraic sum of cuspidal and Eisenstein cohomology. In the present paper we construct regular Eisenstein cohomology classes for…

Let St denote the Steinberg module of $SL_n(Q)$ tensored with Q. Let Sh denote the sharbly resolution of St. By Borel-Serre duality, $H^{n(n-1)/2-i}(SL_n(Z),Q)$ is isomorphic to $H_i(SL_n(Z),St)$. The latter is isomorphic to the homology of…

We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th central derivative of non-singular Fourier coefficients of a normalized Siegel--Eisenstein series, and (2) the degree of special…

We show that the pseudoeffective cone of $k$-cycles on a complete complexity one $T$-variety is rational polyhedral for any $k$, generated by classes of $T$-invariant subvarieties. When $X$ is also rational, we give a presentation of the…

In this paper we consider certain families of arithmetic subgroups of SO^0(p,q) and SL_3(R), respectively. We study the cohomology of such arithmetic groups with coefficients in arithmetically defined modules. We show that for natural…

We prove a number of results on the structure and representation theory of the rational Cherednik algebra of the imprimitive reflection group $G(\ell,p,n)$. In particular, we: (1) show a relationship to the Coulomb branch construction of…

The paper deals with three topics on coquasitriangular bialgebras. A characterization of universal r-forms in terms of Yetter-Drinfeld modules is given. All universal r-forms for the coordinate Hopf algebras of the quantum groups GL_q(N),…

We consider the connections among algebraic cycles, abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed two new obstructions to stable rationality for rationally…

We confirm a conjecture of Quillen in the case of the mod $2$ cohomology of arithmetic groups ${\rm SL}_2({\mathcal{O}}_{\mathbb{Q}(\sqrt{-m})}[\frac{1}{2}]\thinspace)$, where ${\mathcal{O}}_{\mathbb{Q}(\sqrt{-m}\thinspace)}$ is an…

The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure. This book explores a "linearization"…

Let $K$ be an imaginary quadratic field different from $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. For a positive integer $N$, let $K_\mathfrak{n}$ be the ray class field of $K$ modulo $\mathfrak{n}=N\mathcal{O}_K$. By using the…

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…

We construct one-parameter deformations of the Euclidean sphere $\mathbb{S}^n$ inside $\mathbb{R}^{n+1}$ that admit a Zoll family of codimension one embedded minimal spheres, in all dimensions $n\geq 3$. The method of construction is…

We describe how certain cyclotomic Nazarov-Wenzl algebras occur as endomorphism rings of projective modules in a parabolic version of BGG category O of type $D$. Furthermore we study a family of subalgebras of these endomorphism rings which…

We construct varieties B(r;An) such that a map X -> B(r;An) corresponds to a degree-n \'etale algebra on X equipped with r generating global sections. We then show that when n = 2, i.e., in the quadratic \'etale case, that the singular…

We study the coisotropic subgroup structure of standard SL_q(2,R) and the corresponding embeddable quantum homogeneous spaces. While the subgroups S^1 and R_+ survive undeformed in the quantization as coalgebras, we show that R is deformed…

Given a quiver with potential $(Q,W)$, Kontsevich-Soibelman constructed a Hall algebra on the critical cohomology of the stack of representations of $(Q,W)$. Special cases of this construction are related to work of Nakajima, Varagnolo,…

Given a smooth and separated K(pi,1) variety X over a field k, we associate a "cycle class" in etale cohomology with compact supports to any continuous section of the natural map from the arithmetic fundamental group of X to the absolute…

Let A be an abelian variety and let us fix a Weil cohomology with coefficients in F. Let $H^1(A,F)$ be the first cohomology group of A and $Lef(A) \subset GL(H^1(A,F))$ be its Lefschetz group, i.e. the sub-group of $GL(H^1(A,F))$ of linear…

Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak h$ and Weyl group $W$. We build up a graded map $(\mathcal H\otimes \bigwedge\mathfrak h\otimes \mathfrak h)^W\to (\bigwedge \mathfrak g\otimes \mathfrak…