Related papers: Remarks on generating series for special cycles

We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings…

We show that the cohomology ring of a finite-dimensional complex pointed Hopf algebra with an abelian group of group-like elements is finitely generated. Our strategy has three major steps. We first reduce the problem to the finite…

This paper studies the Chow and cohomology rings of the Hacking moduli stack $\mathcal{P}^{\mathrm{H}}$ of plane quartics. We construct a smooth proper Deligne--Mumford stack resolving the Calabi--Yau wall crossing between the KSBA and…

We study generalized special cycles on Hermitian locally symmetric spaces $\Gamma \backslash D$ associated to the groups $G=\mathrm{U}(p,q)$, $\mathrm{Sp}(2n,\mathbb{R}) $ and $\mathrm{O}^*(2n)$. These cycles are (covered by) locally…

We introduce `canonical' classes in the Selmer groups of certain Galois representations with a conjugate-symplectic symmetry. They are images of special cycles in unitary Shimura varieties, and defined uniquely up to a scalar. The…

The invariant subalgebra H^+ of the Heisenberg vertex algebra H under its automorphism group Z/2Z was shown by Dong-Nagatomo to be a W-algebra of type W(2,4). Similarly, the rank n Heisenberg vertex algebra H(n) has the orthogonal group…

A general specialization map is constructed for higher Chow groups and used to prove a "going-up" theorem for algebraic cycles and their regulators. The results are applied to study the degeneration of the modified diagonal cycle of Gross…

We study the restriction map to the closed fiber of a regular projective scheme over an excellent henselian discrete valuation ring, for a cohomological version of the Chow group of relative zero-cycles. Our main result extends the work of…

As an attempt to understand motives over $k[x]/(x^m)$, we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. R\"ulling on 0-dimensional cycles. We give an…

The cohomology ring of the moduli space of stable holomorphic vector bundles of rank n and degree d over a Riemann surface of genus g>1 has a standard set of generators when n and d are coprime. When n=2 the relations between these…

For each simply connected, simple complex group $G$ we show that the direct sum of all vector bundles of conformal blocks on the moduli stack $\bar{\mathcal{M}}_{g, n}$ of stable marked curves carries the structure of a flat sheaf of…

Let $G$ be a finite group and $k$ a field of characteristic $p$. We conjecture that if $M$ is a $kG$-module with $H^*(G,M)$ finitely generated as a module over $H^*(G,k)$ then as an element of the stable module category…

We consider a certain class of Schubert varieties of the affine Grassmannian of type A. By embedding a Schubert variety into a finite-dimensional Grassmannian, we construct an explicit basis of sections of the basic line bundle by…

We construct an anticyclotomic Euler system for the Asai Galois representation associated to $p$-ordinary Hilbert modular forms over real quadratic fields. We also show that our Euler system classes vary in $p$-adic Hida families. The…

Let $V=Spec(R)$ and $R$ be a complete discrete valuation ring of mixed characteristic $(0,p)$. For any flat $R$-scheme $X$ we prove the compatibility of the de Rham fundamental class of the generic fiber and the rigid fundamental class of…

We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results…

This article extends the study of cyclic ramified covers of the projective line defined by Kummer equations. We consider the most general case of such covers, allowing arbitrary orders in the roots of the generating radicant. The primary…

We study maps from a smooth scheme to a motivic sphere in the Morel-Voevodsky ${\mathbb A}^1$-homotopy category, i.e., motivic cohomotopy sets. Following Borsuk, we show that, in the presence of suitable hypotheses on the dimension of the…

We present a conjecture for the Chow ring of the universal moduli stack of bundles over hyperelliptic curves and prove it for rank and genus two. Consequently, we obtain explicit generators and relations to conclude that the Chow ring is…

For a von Neumann algebra M on a Hilbert space, A. Connes has constructed a module S and a derivation of M into S, such that M is approximately finite dimensional if and only if that derivation is inner. The paper contains a generalization…