Examples and Counterexamples for Existence of Categorical Quotients

2000/02/12 by A. A'Campo-Neuen, J. Hausen
Mathematics · #math.AG #msc:14L30 #msc:14D25 #msc:14M25

paper · pdf

published as J. Algebra 231, 67-85 (2000) · 15 pages, 3 figures, LaTeX2e + pstex

arxiv created 2000/02/12 · arxiv updated 2009/11/30

Abstract

We give examples for existence and non-existence of categorical quotients for algebraic group actions in the categories of algebraic varieties and prevarieties. All our examples are subtorus actions on toric varieties.

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• Weakly Proper Toric Quotients
• A categorical quotient in the category of dense constructible subsets
• Quotients of Divisorial Toric Varieties
• Toric Prevarieties and Subtorus Actions
• Topologies de Grothendieck, descente, quotients