Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
The Complexity of a Flat Groupoid
Univ Rennes 1, IRMAR, Campus Beaulieu, F-35042 Rennes, France..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2505-6417
Leiden Univ, Snellius Bldg,Niels Bohrweg 1, NL-2333 CA Leiden, Netherlands..
2018 (English)In: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 23, p. 1157-1196Article in journal (Refereed) Published
Abstract [en]

Grothendieck proved that any finite epimorphism of noetherian schemes factors into a finite sequence of effective epimorphisms. We define the complexity of a flat groupoid R paired right arrows X with finite stabilizer to be the length of the canonical sequence of the finite map R -> X x (X/R) X, where X/R is the Keel-Mori geometric quotient. For groupoids of complexity at most 1, we prove a theorem of descent along the quotient X -> X/R and a theorem on the existence of the quotient of a groupoid by a normal subgroupoid. We expect that the complexity could play an important role in the finer study of quotients by groupoids.

Place, publisher, year, edition, pages
FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur , 2018. Vol. 23, p. 1157-1196
Keywords [en]
Groupoids, group schemes, quotients, algebraic spaces, effective epimorphisms, descent
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-252941ISI: 000468272500035Scopus ID: 2-s2.0-85068109695OAI: oai:DiVA.org:kth-252941DiVA, id: diva2:1323369
Note

QC 20190612

Available from: 2019-06-12 Created: 2019-06-12 Last updated: 2019-08-02Bibliographically approved

Open Access in DiVA

No full text in DiVA

Scopus

Authority records BETA

Rydh, David

Search in DiVA

By author/editor
Rydh, David
By organisation
Mathematics (Div.)
In the same journal
Documenta Mathematica
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 3 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf