{"paper":{"title":"On the depth of quotients of modular invariant rings by transfer ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jonathan Elmer, M\\\"ufit Sezer","submitted_at":"2018-06-28T13:20:29Z","abstract_excerpt":"Let $G$ be a finite group, and $V$ a finite dimensional vector space over a field $k$ of characteristic dividing the order of $G$. Let $H \\leq G$. The transfer map $k[V]^H \\rightarrow k[V]^G$ is an important feature of modular invariant theory. Its image is called a transfer ideal $I^G_H$ of $k[V]^G$, and this ideal, along with the quotients $k[V]^G/I^G_H$ are widely studied.\n  In this article we study $k[V]^G/I$, where $I$ is any sum of transfer ideals. Our main result gives an explicit regular sequence of length $\\dim(V^G)$ in $k[V]^G/I$ when $G$ is a $p$-group. We identify situations where "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10946","kind":"arxiv","version":1},"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"}