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Uniform twisted homological stability
Jeremy Miller, Peter Patzt, Dan Petersen +1
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequen…
Homological vanishing for the Steinberg representation II: reductive groups and integral conjectures
Jeremy Miller, Peter Patzt, Andrew Putman
We prove that the homology groups of any connected reductive group over a field with coefficients in the Steinberg representation vanish in a range. The generalizes work of Ash-Put…
Corrigendum to "Stability in the high-dimensional cohomology of congruence subgroups" [Compos. Math. 156 (2020), no. 4, 822-861]
Jeremy Miller, Rohit Nagpal, Peter Patzt
After the publication of [Compos. Math. 156 (2020), no. 4, 822-861], Andrew Putman pointed out a mistake in our paper and helped us fix it. In this note, we will explain what this…
On rank filtrations of algebraic K-theory and Steinberg modules
Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson
Motivated by his work on the stable rank filtration of algebraic K-theory spectra, Rognes defined a simplicial complex called the common basis complex and conjectured that this com…
On the codimension-two cohomology of
Benjamin Brück, Jeremy Miller, Peter Patzt +2
Borel-Serre proved that is a virtual duality group of dimension and the Steinberg module is its dualizing modu…
Hopf algebras, Steinberg modules, and the unstable cohomology of and
Avner Ash, Jeremy Miller, Peter Patzt
We prove that the direct sum of all homology groups of the integral general linear groups with Steinberg module coefficients form a commutative Hopf algebra, in particular a free g…