Higher derivations of wildly ramified $v$-rings

Configuration Spaces for Wildly Ramified Covers

The classification for wildly ramified covers is more mysterious than for tame covers. A natural configuration space — the space of unordered branch points of a cover — for tame covers allows the construction of Hurwitz spaces, and an often very effective theory for families of tame covers. We define invariants generalizing Nielsen classes for Hurwitz families. The result is a configuration spa...

Higher derivations on rings and modules

Let τ be a hereditary torsion theory on ModR and suppose that Qτ : ModR → ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ : M →M is the colocalization functor, the...

Convergent Higher Derivations on Local Rings

Factorisability and the arithmetic of wildly ramified Galois extensions

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On the Modularity of Wildly Ramified Galois Representations

where GQ = Gal ( Q/Q ) is the absolute Galois group of Q and ` is a fixed rational prime. For example, ρ = ρE,` may be the `-adic representation of an elliptic curve E over Q, or ρ = ρf may be the `-adic representation associated to a modular form. The continuity of such Galois representations implies the image lies in GL2(O) for some ring of integers O with maximal ideal λ in a finite extensio...