Local Systems on Diamonds and <i>p</i>-Adic Vector Bundles

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

Notes on Vector Bundles

−→ V, (v1, v2) −→ v1+v2, are smooth. Note that we can add v1, v2∈V only if they lie in the same fiber over M , i.e. π(v1)=π(v2) ⇐⇒ (v1, v2) ∈ V ×M V. The space V ×M V is a smooth submanifold of V ×V , as follows immediately from the Implicit Function Theorem or can be seen directly. The local triviality condition means that for every point m∈M there exist a neighborhood U of m in M and a diffeo...

Vector bundles on Orbispaces

Orbispaces are spaces with extra structure. The main examples come from compact Lie group actionsX G and are denoted [X/G], their underlying space being X/G. By definition, every orbispace is locally of the form [X/G], but the group G might vary. To be more precise, an orbispace is a topological stack which is locally equivalent to [X/G] for G a Lie group and X a G-CW-complex [2] [4] [5]. Howev...

Higgs Bundles and Local Systems on Riemann Surfaces

1. Preface 1 2. The Dolbeault Moduli Space 3 2.1. Higgs bundles 3 2.2. The moduli space 8 2.3. The Hitchin-Kobayashi correspondence 13 3. The Betti Moduli Space 22 3.1. Representation varieties 22 3.2. Local systems and holomorphic connections 23 3.3. The Corlette-Donaldson theorem 27 3.4. Hyperkähler reduction 32 4. Differential Equations 34 4.1. Uniformization 34 4.2. Higher order equations 3...

Generalized bc-systems based on Hermitian vector bundles

A generalized bc-system associated to a Hermitian vector bundle over a Riemann surface is introduced in close analogy to the usual rank one case. Some of the geometric analogies to the well-known case are studied. In particular, if there are no zero-modes, the \nonabelian" theta divisor appears. In the general case where zero-modes exist, it seems to be more diicult to nd a natural description....