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Operations on Étale Sheaves of Sets
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Operationer på étala kärvar av mängder (Swedish)
Abstract [en]

Rydh showed in 2011 that any unramified morphism ƒof algebraic spaces (algebraic stacks) has a canonical and universal factorization through an algebraic space (algebraic stack) called the étale envelope of ƒ, where the first morphism is a closed immersion and the second is étale. We show that when ƒ is étale then the étale envelope can be described by applying the left adjoint of the pullback of ƒ to the constant sheaf defined by a pointed set with two elements. When ƒ is a monomorphism locally of finite type we have a similar construction using the direct image with proper support.

Abstract [sv]

Rydh visade 2011 att varje oramifierad morfi ƒ av algebraiska rum (algebraiska stackar) har en kanonisk och universell faktorisering genom ett algebraiskt rum (algebraisk stack) som han kallar den étala omslutningen av ƒ, där den första morfin är en sluten immersion och den andra är étale. Vi visar att då ƒ är étale så kan den étala omslutningen beskrivas genom att applicera vänsteradjunkten till tillbakadragningen av ƒ på den konstanta kärven som definieras av en punkterad mängd med två element. Då ƒ är en monomorfi, lokalt av ändlig typ så har vi en liknande beskrivning i termer av framtryckning med propert stöd.

Place, publisher, year, edition, pages
2016.
Series
TRITA-MAT-E, 2016:26
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-188412OAI: oai:DiVA.org:kth-188412DiVA: diva2:938522
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2016-06-17 Created: 2016-06-09 Last updated: 2016-06-17Bibliographically approved

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CiteExportLink to record
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