Compatible systems and ramification

Compatible Systems and Correspondences

Classification of Ramification Systems for Symmetric Groups

We obtain the formula computing the number of isomorphic classes of ramification systems with characters over group Sn (n 6= 6) and their representatives. 2000 Mathematics Subject Classification: 16W30, 05H99.

Bigness in Compatible Systems

Clozel, Harris and Taylor have recently proved a modularity lifting theorem of the following general form: if ρ is an l-adic representation of the absolute Galois group of a number field for which the residual representation ρ comes from a modular form then so does ρ. This theorem has numerous hypotheses; a crucial one is that the image of ρ must be “big,” a technical condition on subgroups of ...

Ramification and Causality

In formal systems for reasoning about actions, the ramification problem denotes the problem of handling indirect effects. These effects are not explicitly represented in action specifications but follow from general laws describing dependencies among components of the world state. An adequate treatment of indirect effects requires a suitably weakened version of the general law of persistence. I...

Compatible Factorizations and Three-fold Triple Systems

A three-fold triple system is a design wherein each pair of treatments occurs exactly once. One way to construct this design is by using an idempotent commutative quasigroup. This paper attempts to provide another method of constructing a 3-fold triple system. Firstly, we would like to discuss compatible factorization without multiple edges using a patterned starter construction. Then, we will ...