{"paper":{"title":"Ghosts in modular representation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.RT","authors_text":"Jan Minac, J. Daniel Christensen, Sunil K. Chebolu","submitted_at":"2006-09-25T15:46:16Z","abstract_excerpt":"A ghost over a finite p-group G is a map between modular representations of G which is invisible in Tate cohomology. Motivated by the failure of the generating hypothesis---the statement that ghosts between finite-dimensional G-representations factor through a projective---we define the ghost number of kG to be the smallest integer l such that the composition of any l ghosts between finite-dimensional G-representations factors through a projective. In this paper we study ghosts and the ghost numbers of p-groups. We begin by showing that a weaker version of the generating hypothesis, where the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609699","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}