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On the Smoothness of the Quot Functor
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

For a commutative ring k,we consider free k-modules E, endowing them with k[x_1,...,x_m]-module structuresthrough a ring homomorphism k[x_1,...,x_m] -> End_Z(E). These structures arethen inspected by encoding the actions of the unknowns x_i in matricesX_1,...,X_m. We further introduce the concepts of lifts and formal smoothnessfor functors, and define the Quot_{F/A/k}^n functor acting on the category ofk-algebras, taking some k-algebra B to the set of quotients of the form (F ⊗_k B)/N, which are locallyfree as B-modules. Lastly, we find concrete examples of modules showing thatthe functors Hilb_{k[x,y,z]/k}^4 and Quot_{⊕^2 k[x,y]/k[x,y]/k}^2 are not formally smooth

Place, publisher, year, edition, pages
2013. , 32 p.
Series
TRITA-MAT-E, 2013:29
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-123658OAI: oai:DiVA.org:kth-123658DiVA: diva2:630453
Subject / course
Mathematics
Educational program
Master of Science - Engineering Mechanics
Supervisors
Examiners
Available from: 2013-06-19 Created: 2013-06-13 Last updated: 2013-06-19Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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