Related papers: On p-adic intermediate Jacobians

We prove, using $p$-adic Hodge theory for open algebraic varieties, that for a smooth projective variety over a subfield $k\subset\mathbb C$ which is of finite type over $\mathbb Q$, the complex abel jacobi map vanishes if the etale abel…

We reformulate the notion of a Jacobi algebroid in terms of weighted odd Jacobi brackets. We then show how a Jacobi algebroid can be understood in terms of a kind of curved Q-manifold. In particular the homological condition on the odd…

Let $X$ be a complex torus of dimension $g$ and $\hat{X}$ be the dual torus. For any $g(g-1)/2$-tuple $\lambda$ of complex numbers of absolute value $1$, we define a non-commutative complex torus $X_\lambda$ as a sheaf of algebras on a real…

We construct and study the moduli of continuous representations of a profinite group with integral $p$-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is…

We establish a "matrix simultaneous diagonalization theorem" for disconnected reductive groups which relaxes both the semisimplicity condition and the commutativity condition. As an application, we prove the following basic results…

In this paper we study a $k$-dimensional analytic subvariety of the complex algebraic torus. We show that if its logarithmic limit set is a finite rational $(k-1)$-dimensional spherical polyhedron, then each irreducible component of the…

We study the structure of the category of graded, connected, countable-dimensional, commutative and cocommutative Hopf algebras over a perfect field $k$ of characteristic $p$. Every $p$-torsion object in this category is uniquely a direct…

Let X be a smooth projective curve of genus >1 over a field K which is finitely generated over the rationals. The section conjecture in Grothendieck's anabelian geometry says that the sections of the canonical projection from the arithmetic…

We prove modularity of certain residually reducible ordinary 2-dimensional $p$-adic Galois representations with determinant a finite order odd character $\chi$. For certain non-quadratic $\chi$ we prove an $R=T$ result for $T$ the weight 1…

$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic…

We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of C_p. It takes values in a mixed-characteristic analogue of Dieudonne modules, which was previously defined by Fargues as a version of…

We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for classifying the full Poisson automorphism groups of…

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 -…

For $C$ a complete algebraically closed extension of $\mathbb{Q}_p$, we show that a one-dimensional $p$-divisible group $G/ \mathcal{O}_C$ can be defined over a complete discretely valued subfield $L \subset C$ with Hodge-Tate period ratios…

For $G$ a symplectic or orthogonal $p$-adic group (not necessarily split), or an inner form of a general linear $p$-adic group, we compute the endomorphism algebras of some induced projective generators \`a la Bernstein of the category of…

For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced…

We interpret syntomic cohomology of Nekov\'a\v{r}-Nizio{\l} as a $p$-adic absolute Hodge cohomology. This is analogous to the interpretation of Deligne-Beilinson cohomology as an absolute Hodge cohomology by Beilinson and generalizes the…

We relate various approaches to coefficient systems in relative integral $p$-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over…

Consider a genus 2 curve defined over $\mathbb{Q}$ given by an affine equation of the form $y^2 = f(x)$ for some polynomial $f$ of degree 5, and let $p$ be an odd prime. Extending work of Perrin-Riou for elliptic curves, we construct a…

The classical Rees construction (of common use in commutative algebra and Hodge theory) interpolates between filtrations, viewed as ${\mathbb G}_m$-equivariant vector bundles on the affine line, and their associated gradings. Various…