3 papers
math.NT2025
Cohomology at Infinity and the Well-Tempered Complex
Dylan Galt, Mark McConnell
We prove the existence of a sequence of commutative diagrams generalizing existing results on the cohomology of the Borel-Serre boundary and well-rounded retract to the context of…
math.GT2024
Explicit sharbly cycles at the virtual cohomological dimension for SL_n(Z)
Avner Ash, Paul E. Gunnells, Mark McConnell
Denote the virtual cohomological dimension of SL_n(Z) by t=n(n-1)/2. Let St denote the Steinberg module of SL_n(Q) tensored with Q. Let Sh_* denote the sharbly resolution of the St…
math.NT2024
Cohomology with Sym^g coefficients for congruence subgroups of SL_4(Z) and Galois representations
Avner Ash, Paul E. Gunnells, Mark McConnell
We extend the computations in our prior work to find the cohomology in degree five of a congruence subgroup Gamma of SL_4(Z) with coefficients in Sym^g(K^4), twisted by a nebentype…