Cohomology of local systems on loci of d-elliptic abelian surfaces

We consider the loci of d-elliptic curves in $M_2$, and corresponding loci of d-elliptic surfaces in $A_2$. We show how a description of these loci as quotients of a product of modular curves can be used to calculate cohomology of natural local systems on them, both as mixed Hodge structures and $\ell$-adic Galois representations. We study in particular the case d=2, and compute the Euler characteristic of the moduli space of n-pointed bi-elliptic genus 2 curves in the Grothendieck group of Hodge structures.Comment: 15 pages, complete re-write of earlier versio

Designing People to Serve

I argue that, contrary to intuition, it would be both possible and permissible to design people - whether artificial or organic - who by their nature desire to do tasks we find unpleasant

Banishment Of Non-Natives By Alaska Native Tribes: A Response To Alcoholism And Drug Addiction Halley Petersen

Since 2015, at least a dozen tribal court banishments have been reported in Alaska, mainly involving alleged bootleggers and drug dealers in rural communities. Rural Alaska communities, which are predominantly Alaska Native, face high rates of alcoholism, drug abuse, and related crime. Faced with these drug and alcohol issues and insufficient access to law enforcement, it is not surprising that some communities have decided to banish offenders. However, banishment is not currently legal, at least when imposed upon non-Native citizens. Tribal courts lack sufficient jurisdiction over non-Natives to banish them for bootlegging or dealing drugs. Tribal governments are sovereigns with inherent powers, but they are subject to certain restrictions under the federal government. Land-based jurisdiction is insufficient to claim jurisdiction in these cases because Alaska lacks significant Indian country and the Montana factors fail to provide definitive support. Tribal jurisdiction, however, should be expanded to allow tribal courts to banish non-Natives for violations of drug and alcohol laws to improve access to justice, decrease the burden on state law enforcement, and improve welfare in rural Alaskan communities

Cohomology of generalized configuration spaces

Let $X$ be a topological space. We consider certain generalized configuration spaces of points on $X$, obtained from the cartesian product $X^n$ by removing some intersections of diagonals. We give a systematic framework for studying the cohomology of such spaces using what we call "tcdga models" for the cochains on $X$. We prove the following theorem: suppose that $X$ is a "nice" topological space, $R$ is any commutative ring, $H^\bullet_c(X,R)\to H^\bullet(X,R)$ is the zero map, and that $H^\bullet_c(X,R)$ is a projective $R$-module. Then the compact support cohomology of any generalized configuration space of points on $X$ depends only on the graded $R$-module $H^\bullet_c(X,R)$. This generalizes a theorem of Arabia.Comment: 47 pages. V2: significant revision, inaccuracies corrected. Final versio

U.S. Infringement Liability for Foreign Sellers of Infringing Products

With the ever-increasing international flavor of business comes an important question for United States patent holders and foreign manufacturers alike: Can a company be held liable for patent infringement in the United States for selling an infringing product abroad that is later imported into the United States