19 citations · 106 across the 21 of their papers we have counts for
16 papers · 1 filter
The Morita classes are nonzero
Alexander Kupers, Jeremy Miller, Peter Patzt
We prove that all Morita classes are nonzero using a novel description of the Hopf algebra structure on Steinberg homology. We prove anal…
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…
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…
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…
A presentation of symplectic Steinberg modules and cohomology of
Benjamin Brück, Peter Patzt, Robin J. Sroka
Borel-Serre proved that the integral symplectic group is a virtual duality group of dimension and that the symplectic Steinberg module $\…
The homology of the partition algebras
Rachael Boyd, Richard Hepworth, Peter Patzt
We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with…
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…
Improved homological stability for certain general linear groups
Alexander Kupers, Jeremy Miller, Peter Patzt
We prove that the general linear groups of the integers, Gaussian integers, and Eisenstein integers satisfy homological stability of slope 1 when using -coefficien…
The homology of the Brauer algebras
Rachael Boyd, Richard Hepworth, Peter Patzt
This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our…
On the generalized Bykovskii presentation of Steinberg modules
Alexander Kupers, Jeremy Miller, Peter Patzt +1
We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of…
Representation stability, secondary stability, and polynomial functors
Jeremy Miller, Peter Patzt, Dan Petersen
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many fami…
Non-integrality of some Steinberg modules
Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson +1
We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the gen…
Stability in the high-dimensional cohomology of congruence subgroups
Jeremy Miller, Rohit Nagpal, Peter Patzt
We prove a representation stability result for the codimension-one cohomology of the level three congruence subgroup of . This is a special case of a que…
Central stability for the homology of congruence subgroups and the second homology of Torelli groups
Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson
We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the…