Eric M. Friedlander
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View article: Infinite dimensional modules for linear algebraic groups
Infinite dimensional modules for linear algebraic groups Open
We investigate infinite dimensional modules for a linear algebraic group $\mathbb G$ over a field of positive characteristic $p$. For any subcoalgebra $C \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we consider …
View article: Community-Based Cluster-Randomized Trial to Reduce Opioid Overdose Deaths
Community-Based Cluster-Randomized Trial to Reduce Opioid Overdose Deaths Open
In this 12-month multimodal intervention trial involving community coalitions in the deployment of evidence-based practices to reduce opioid overdose deaths, death rates were similar in the intervention group and the control group in the c…
View article: Reformulation of the stable Adams conjecture
Reformulation of the stable Adams conjecture Open
We revisit methods of proof of the Adams Conjecture in order to correct and supplement earlier efforts to prove analogous conjectures in the stable homotopy category. We utilize simplicial schemes over an algebraically closed field of posi…
View article: Filtrations and Growth of $\mathbb G$-modules
Filtrations and Growth of $\mathbb G$-modules Open
We investigate infinite dimensional modules for an affine group scheme $\mathbb G$ of finite type over a field of positive characteristic $p$. For any subspace $X \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we …
View article: Support varieties and stable categories for algebraic groups
Support varieties and stable categories for algebraic groups Open
We consider rational representations of a connected linear algebraic group $\mathbb {G}$ over a field $k$ of positive characteristic $p > 0$ . We introduce a natural extension $M \mapsto \Pi (\mathbb {G})_M$ to $\mathbb {G}$ -modules of th…
View article: Support theory for Drinfeld doubles of some infinitesimal group schemes
Support theory for Drinfeld doubles of some infinitesimal group schemes Open
Consider a Frobenius kernel G in a split semisimple algebraic group, in very\ngood characteristic. We provide an analysis of support for the Drinfeld center\nZ(rep(G)) of the representation category for G, or equivalently for the\nrepresen…
View article: Brian J. Parshall (October 28, 1945–January 17, 2022)
Brian J. Parshall (October 28, 1945–January 17, 2022) Open
Parshall died suddenly and unexpectedly on
View article: Support Varieties and stable categories for algebraic groups
Support Varieties and stable categories for algebraic groups Open
We consider rational representations of a connected linear algebraic group $\mathbb G$ over a field $k$ of positive characteristic $p > 0$. We introduce a natural extension $M \mapsto Π(\mathbb G)_M$ to $\mathbb G$-modules of the $π$-point…
View article: Support theory for Drinfeld doubles of some infinitesimal group schemes
Support theory for Drinfeld doubles of some infinitesimal group schemes Open
Consider a Frobenius kernel G in a split semisimple algebraic group, in very good characteristic. We provide an analysis of support for the Drinfeld center Z(rep(G)) of the representation category for G, or equivalently for the representat…
View article: Support Theory for Extended Drinfeld Doubles
Support Theory for Extended Drinfeld Doubles Open
Following earlier work with Cris Negron on the cohomology of Drinfeld doubles $D(\mathbb G_{(r)})$, we develop a "geometric theory" of support varieties for "extended Drinfeld doubles" $\tilde D(\mathbb G_{(r)})$ of Frobenius kernels $\mat…
View article: About the cover: Andrei Suslin, 1950–2018
About the cover: Andrei Suslin, 1950–2018 Open
Andrei was my close friend for many years.We first met in Oberwolfach in the late 1970s.Andrei's English was perfect; not only did he speak and understand the language, but he understood subtle nuances, which astonished me.We talked mathem…
View article: The mathematics of Andrei Suslin
The mathematics of Andrei Suslin Open
involved in both the formulation and the solution of many of the most important questions in algebraic K-theory.His own evolution from a "pure algebraist" led to a partnership with Vladimir Voevodsky in building the edifice of motivic coho…
View article: Cohomology for Drinfeld doubles of some infinitesimal group schemes
Cohomology for Drinfeld doubles of some infinitesimal group schemes Open
Consider a field k of characteristic p > 0, G_r the r-th Frobenius kernel of\na smooth algebraic group G, DG_r the Drinfeld double of G_r, and M a finite\ndimensional DG_r-module. We prove that the cohomology algebra H*(DG_r,k) is\nfinitel…
View article: In Memoriam: Vladimir Voevodsky
In Memoriam: Vladimir Voevodsky Open
Vladimir Voevodsky's untimely death continues to be a significant loss to the mathematical research community.It is also a personal loss for me, for I valued Vladimir as a friend and was fortunate to be able to appreciate first hand his ma…
View article: Generalization of LRU Cache Replacement Policy with Applications to\n Video Streaming
Generalization of LRU Cache Replacement Policy with Applications to\n Video Streaming Open
Caching plays a crucial role in networking systems to reduce the load on the\nnetwork and is commonly employed by content delivery networks (CDNs) in order\nto improve performance. One of the commonly used mechanisms, Least Recently\nUsed …
View article: James G. Arthur: AMS 2017 Steele Prize for Lifetime Achievement
James G. Arthur: AMS 2017 Steele Prize for Lifetime Achievement Open
im Arthur's illustrious career, spread out over almost five decades, has contributed in a profound manner to our understanding of the theory of automorphic forms.He has single-handedly developed the trace formula, now known as the "Arthur-…
View article: Cohomology of unipotent group schemes
Cohomology of unipotent group schemes Open
We verify that universal classes in the cohomology of $GL_N$ determine explicit cohomology classes of Frobenius kernels $G_{(r)}$ of various linear algebraic groups $G$ . We consider the relationship of $\varprojlim_r H^*(U_{(r)},k)$ to th…
View article: An approach to intersection theory on singular varieties using motivic complexes
An approach to intersection theory on singular varieties using motivic complexes Open
We introduce techniques of Suslin, Voevodsky, and others into the study of singular varieties. Our approach is modeled after Goresky–MacPherson intersection homology. We provide a formulation of perversity cycle spaces leading to perversit…
View article: Diffusion Approximations for Controlled Weakly Interacting Large Finite\n State Systems with Simultaneous Jumps
Diffusion Approximations for Controlled Weakly Interacting Large Finite\n State Systems with Simultaneous Jumps Open
We consider a rate control problem for an $N$-particle weakly interacting\nfinite state Markov process. The process models the state evolution of a large\ncollection of particles and allows for multiple particles to change state\nsimultane…