Paul Feit

The K-admissibility of SL(2, 5)

Let K be a field and let G be a finite group. G is K-admissible if there exists a Galois extension L of K with G=Gal(L/K) such that L is a maximal subfield of a central K-division algebra. We characterize those number fields K such that H is K-admissible where H is any subgroup of SL(2, 5) which contains a S2-group. The method also yields refinements and alternate proofs of some known results including the fact that A5 is K-admissible for every number field K.

Explicit formulas for local factors in the Euler products for Eisenstein series

Our objective is to prove that certain Dirichlet series (in our variable q −s ) , which are defined by infinite sums, can be expressed as a product of an explicit rational function in q −s times an unknown polynomial M in q −s Moreover we show that M(q −s ) is 1 if a simple condition is met. The Dirichlet series appear in the Euler products of Fourier coefficients for Eisenstein series. The series discussed below generalize the functions α 0 (N, q −s ) used by Shimura in [12], and the theorem is an extension of Kitaoka’s result [5].

Existence of Orbifolds II: Orbifold Structures

This paper is second in a quartology which develops a universal Existence Theorem for orbifolds. In this work, we adapt an existing, universal, construction to the problem. We prove a formal theorem which states that, under a certain hypothesis, a category can be expanded to include new quotients by finite group actions.

A Fundamental Group for Dynamical Systems II: Z p

Abstract This paper continues exploration of a recent homotopy construction for group-sets. It proves that, for p prime, and with respect to regarded as a -set, the homotopy group has a canonical identification with the kernel of the canonical projection from the profinite completion of to .

Følner sequences and Hilbert’s Irreducibility Theorem over Q

AbstractLetf(X; T1, ...,Tn) be an irreducible polynomial overQ. LetB be the set ofb teZn such thatf(X;b) is of lesser degree or reducible overQ. Let ℱ={Fj}{Fj}j−1∞ be a Følner sequence inZn — that is, a sequence of finite nonempty subsetsFj ⊆Zn such that for eachvteZn,

A Fundamental Group for Dynamical Systems III: Simple Compactifications

\mathop {lim}\limits_{j \to \infty } \frac{{\left| {F_j \cap (F_j + \upsilon )} \right|}}{{\left| {F_j } \right|}} = 1

Existence of orbifolds III: Pseudoétale topologies

Suppose ℱ satisfies the extra condition that forW a properQ-subvariety ofPn−An and ɛ>0, there is a neighborhoodU ofW(R) in the real topology such that