arXiv subjects
Publications and source records attributed to Jon Cohen.
The covering number of an associative ring $R$ is the minimal number of proper subrings whose union is $R$. We establish a strategy to classify unital rings of a given finite covering number, and obtain a classification of unital rings whose covering number is four. Along the way we compute the covering number of every finite local ring whose residue field has prime order.
We characterize the Local Langlands Correspondence (LLC) for inner forms of $GL_n$ via the Jacquet-Langlands Correspondence (JLC) and compatibility with the Langlands Classification. We show that LLC satisfies a natural compatibility with parabolic induction and characterize LLC for inner forms as a unique family of bijections $Π(GL_r(D)) \to Φ(GL_r(D))$ for each $r$, (for a fixed $D$) satisfying certain properties. We construct a surjective map of Bernstein centers $\mathfrak{Z}(GL_n(F))\to \mathfrak{Z}(GL_r(D))$ and show this produces pairs of matching distributions. Finally, we construct explicit Iwahori-biinvariant matching functions for unit elements in the parahoric Hecke algebras of $GL_r(D)$, and thereby produce many explicit pairs of matching functions.