Related papers: Canonical lifts and $\delta$-structures

We study a family of surfaces of general type that arises from the intersections of two translates of the theta divisor on a principally polarized complex abelian fourfold. In particular we determine the N\'eron-Severi lattices of these…

Let $\mathrm{G}$ be a symplectic or a split orthogonal group over a local non-archimedean field $\mathrm{F}$. A prime $\ell$ is called banal with respect to $\mathrm{G}$ if it does not divide the cardinality of the $k$-points of…

In 1983 Silverman and Tate showed that the set of points in a 1-dimensional family of abelian varieties where a section of infinite order has `small height' is finite. We conjecture a generalisation to higher-dimensional families, where we…

We prove several results concerning the existence of potentially crystalline lifts with prescribed Hodge-Tate weights and inertial types of a given n-dimensional mod p representation of the absolute Galois group of K, where K/Q_p is a…

In this paper, we prove the existence of certain lifts of Hilbert cusp forms to general odd spin groups. We then use those lifts to provide evidence for a conjecture of Gross on the modularity of abelian varieties not of ${\rm GL}_2$-type.

We use the theta lift to study the multiplicity with which certain automorphic representations of cohomological type occur in a family of congruence covers of an arithmetic manifold. When the family of covers is a so-called `p-adic…

We construct explicit canonical transformations producing non-abelian duals in principal chiral models with arbitrary group G. Some comments concerning the extension to more general $\sigma$-models, like WZW models, are given.

The reduction of Siegel varieties modulo a prime number p is stratified by the multiplicative rank of the p-divisible group of the universal abelian variety. For r\geq 0 the maximal multiplicative subgroup of the restriction of the…

The Kudla lift studied in this article is a classical version for Picard modular forms of the automorphic theta lift between $\text{GU}(2)$ and $\text{GU}(3)$. We construct an explicit $p$-adic analytic family of Picard modular forms…

We prove automorphy lifting results for certain essentially conjugate self-dual $p$-adic Galois representations $\rho$ over CM imaginary fields $F$, which satisfy in particular that $p$ splits in $F$, and that the restriction of $\rho$ on…

Let $Q$ be a $p$-subgroup of a finite $p$-solvable group $G$, where $p$ is a prime, and suppose that $\delta$ is a linear character of $Q$ with the property that $\delta(x)=\delta(y)$ whenever $x,y\in Q$ are conjugate in $G$. In this…

Motivated by the weight part of Serre's conjecture we consider the following question. Let $K/\mathbb{Q}_p$ be a finite extension and suppose $\overline{\rho} \colon G_K \rightarrow \operatorname{GL}_n(\overline{\mathbb{F}}_p)$ admits a…

We introduce a notion of formally \'etale $\mathbb{E}_{\infty}$-coalgebras and show that they admit essentially unique, functorial lifts along square zero extensions of $\mathbb{E}_{\infty}$-rings. Using this, we show that for a perfect…

We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the automorphism group of the cluster category…

The first part of the paper develops the theory of $m$-shifted $\pi$-typical Witt vectors which can be viewed as subobjects of the usual $\pi$-typical Witt vectors. We show that the shifted Witt vectors admit a delta structure that satisfy…

We define a regularized lift from harmonic weak Maass forms of weight $2-N$ to differential forms of degree $N-1$ on the symmetric space $\SL_N(\R)/\SO(N)$, that are smooth outside of certain modular symbols. We show that this lift is…

For a finite extension $K/\mathbb{Q}_p$ and a split reductive group $G$ over $\mathcal{O}_K$, let $\overline{\rho} \colon \mathrm{Gal}_K \to G(\overline{\mathbb{F}}_p)$ be a continuous quasi-semisimple mod $p$ $G$-valued representation of…

We prove a precise version of a theorem of Siu and Beauville on morphisms to higher genus curves, and use it to show that if a variety $X$ in characteristic $p$ lifts to characteristic $0$, then any morphism $X \to C$ to a curve of genus $g…

This paper investigates the transfer of classical geometric structures from a smooth manifold $M$ to its Weil bundle $(M^\mathbf A, \tilde\pi_M, M)$ associated with a Weil algebra $\mathbf A$. We show that various structures including…

Given two finite covers $p: X \to S$ and $q: Y \to S$ of a connected, oriented, closed surface $S$ of genus at least $2$, we attempt to characterize the equivalence of $p$ and $q$ in terms of which curves lift to simple curves. Using…