Monodromy Groups and Self-Invariance

Monodromy Groups and Poincaré Series

Iterated Monodromy Groups

We associate a group IMG(f) to every covering f of a topological space M by its open subset. It is the quotient of the fundamental group π1(M) by the intersection of the kernels of its monodromy action for the iterates fn. Every iterated monodromy group comes together with a naturally defined action on a rooted tree. We present an effective method to compute this action and show how the dynamic...

Independence of ` of Monodromy Groups

Let X be a smooth curve over a finite field of characteristic p. Let E be a number field, and consider an E-compatible system L = {Lλ} of lisse sheaves on X . This means that for every place λ of E not lying over p, we are given a lisse Eλ-sheaf Lλ on X , and these lisse sheaves are E-compatible with one another in the sense that, for every closed point x of X , the polynomial det(1 − T Frobx,L...

LOCAL MONODROMY OF p-DIVISIBLE GROUPS

A p-divisible group over a field K admits a slope decomposition; associated to each slope λ is an integer m and a representation Gal(K) → GLm(Dλ), where Dλ is the Qp-division algebra with Brauer invariant [λ]. We call m the multiplicity of λ in the p-divisible group. Let G0 be a p-divisible group over a field k. Suppose that λ is not a slope of G0, but that there exists a deformation of G in wh...

Monodromy groups of irregular elliptic surfaces

Monodromy groups, i.e. the groups of isometries of the intersection lattice LX := H2/torsion generated by the monodromy action of all deformation families of a given surface, have been computed in [Lö’] for any minimal elliptic surface with pg > q = 0. New and refined methods are now employed to address the cases of minimal elliptic surfaces with pg ≥ q > 0. Thereby we get explicit families suc...