skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Patzt, Peter"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; ; ; (, Advances in Mathematics)
    Borel–Serre proved that SL_n(Z) is a virtual duality group of dimension (n choose 2) and the Steinberg module St_n(Q) is its dualizing module. This module is the top-dimensional homology group of the Tits building associated to SL_n(Q). We determine the “relations among the relations” of this Steinberg module. That is, we construct an explicit partial resolution of length two of the SL_n(Z)-module St_n(Q). We use this partial resolution to show the codimension-2 rational cohomology group of SLn(Z) vanishes for n ≥ 3. This resolves a case of a conjecture of Church–Farb–Putman. We also produce lower bounds for the codimension-1 cohomology of certain congruence subgroups of SLn(Z). 
    more » « less
    Full Text Available 
  2. ; ; (, Geometry & Topology)
    null (Ed.)
    Full Text Available 
  3. ; ; ; (, International Mathematics Research Notices)
    Full Text Available 
  4. ; ; (, Compositio Mathematica)
    We prove a representation stability result for the codimension-one cohomology of the level-three congruence subgroup of $$\mathbf{SL}_{n}(\mathbb{Z})$$ . This is a special case of a question of Church, Farb, and Putman which we make more precise. Our methods involve proving finiteness properties of the Steinberg module for the group $$\mathbf{SL}_{n}(K)$$ for $$K$$ a field. This also lets us give a new proof of Ash, Putman, and Sam’s homological vanishing theorem for the Steinberg module. We also prove an integral refinement of Church and Putman’s homological vanishing theorem for the Steinberg module for the group $$\mathbf{SL}_{n}(\mathbb{Z})$$ . 
    more » « less
    Full Text Available 
  5. ; ; (, Advances in Mathematics)
    Full Text Available 
  6. ; ; ; (, Journal of Topology)