Parallel transport for vector bundles on $p$-adic varieties

p-adic vector bundles on curves and abelian varieties and representations of the fundamental group

A Splitting Criterion for Vector Bundles on Higher Dimensional Varieties

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on arbitrary smooth complex projective varieties of dimension ≥ 4, which asserts that a vector bundle E on X splits iff its restriction E|Y to an ample smooth codimension 1 subvariety Y ⊂ X splits.

Splitting Criteria for Vector Bundles on Higher Dimensional Varieties

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension ≥ 4, over which every extension of line bundles splits.

Z/p metabelian birational p-adic section conjecture for varieties

In this manuscript we generalize the Z/p metabelian birational p-adic Section Conjecture for curves, as introduced and proved in Pop [P2], to all complete smooth varieties. As a consequence one gets a minimalistic p-adic analog of the famous Artin–Schreier theorem on the Galois characterization of the orderings of fields.

Vector Bundles over Analytic Character Varieties

Let Qp ⊆ L ⊆ K ⊆ Cp be a chain of complete intermediate fields where Qp ⊆ L is finite and K discretely valued. Let Z be a one dimensional finitely generated abelian locally L-analytic group and let ẐK be its rigid Kanalytic character group. Generalizing work of Lazard we compute the Picard group and the Grothendieck group of ẐK . If Z = o, the integers in L 6= Qp, we find Pic(ôK) = Zp which ans...