For a complex abelian surface A with endomorphism ring isomorphic to the maximal order in a quartic CM-field K, the Igusa invariants j1(A), j2(A), j3(A) generate an unramified abelian extension of the reflex field of K. In this paper we give an explicit geometric description of the Galois action of the class group of this reflex field on j1(A), j2(A), j3(A). Our description can be expressed by ...

Correspondence: [email protected] Chair for Computation in Engineering, Technische Universität München, Arcisstraße 21, 80333 München, Germany Full list of author information is available at the end of the article Abstract Recently, a multi-level hp-version of the Finite Element Method (FEM) was proposed to ease the difficulties of treating hanging nodes, while providing full hp-approximat...

We present a new game-theoretic framework where Bayesian players engage in a Markov game and each has private but imperfect information regarding other players’ types. Instead of utilizing Harsanyi’s abstract types and a common prior distribution, we construct player types whose structure is explicit and induces a finite level belief hierarchy. We characterize equilibria in this game and formal...

Let f be a normalized eigenform of level N` for some positive integer α and some odd prime ` satisfying gcd(`, n) = 1. A construction of Deligne, Shimura, et. al., attaches an `-adic continuous two-dimensional Galois representation to f . The Refined Conjecture of Serre states that such a representation should in fact arise from a normalized eigenform of level prime to `. In this thesis we pres...