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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.
TRITA-MAT-E, 2013:29
National Category
URN: urn:nbn:se:kth:diva-123658OAI: diva2:630453
Subject / course
Educational program
Master of Science - Engineering Mechanics
Available from: 2013-06-19 Created: 2013-06-13 Last updated: 2013-06-19Bibliographically approved

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