Revisiting the Afterlife: The Inadequacies of Heaven and Hell

This paper deals with some of the ambiguities that are associated with the intermediate and final states after death. Whereas many in the church have dismissed these concepts as myths of the ancients, this discussion shows how the grounding of such beliefs in the Hebrew mindset was the key to Jesus’ own teachings about the afterlife. The argument begins by developing a biblical anthropology over against the modern naturalistic anthropologies that have largely dominated the philosophical and theological scenes. From here we look at the Old Testament concept of the afterlife, and how the modern view that the Hebrews were ambivalent about such a concept is plainly false. Then it is argued that the New Testament doctrines of heaven and hell, which become very specific at this point, are thoroughly indebted to Jewish underpinnings. Without this foundation there would be no clear divisions within the realms of the dead, but because Jesus and his followers assume the validity of the Old Testament material they are able to flesh out such eschatological questions as where Jesus went after death, and where the saint and reprobate will go today. Far from being a stale theological issue, this study has direct bearing upon how one evangelizes today. For when the specific concepts are grasped, the believer will realize that the lost are not going to hell, at least not yet

Which finite simple groups are unit groups?

We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $2^k -1$ for some $k$; or (c) a projective special linear group $PSL_n(\mathbb{F}_2)$ for some $n \geq 3$. Moreover, these groups do (trivially) all occur as unit groups. We deduce this classification from a more general result, which holds for groups $G$ with no non-trivial normal 2-subgroup

Newton slopes for Artin-Schreier-Witt towers

We fix a monic polynomial $f(x) \in \mathbb F_q[x]$ over a finite field and consider the Artin-Schreier-Witt tower defined by $f(x)$; this is a tower of curves $\cdots \to C_m \to C_{m-1} \to \cdots \to C_0 =\mathbb A^1$, with total Galois group $\mathbb Z_p$. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function form arithmetic progressions which are independent of the conductor of the character. As a corollary, we obtain a result on the behavior of the slopes of the eigencurve associated to the Artin-Schreier-Witt tower, analogous to the result of Buzzard and Kilford.Comment: 15 pages, upon the refereed version (to appear in Math. Ann), we fixed two minor errors, one in the proof of Theorem 3.8, the other for Theorem 4.