Browsing NTNU Open by Author "Bergh, Petter Andreas"
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Realizability and the AvruninScott theorem for higherorder support varieties
Bergh, Petter Andreas; Jorgensen, David Alan (Journal article; Peer reviewed, 2018)We introduce higherorder support varieties for pairs of modules over a commutative local complete intersection ring and give a complete description of which varieties occur as such support varieties. In the context of a ... 
Separable equivalences, finitely generated cohomology and finite tensor categories
Bergh, Petter Andreas (Peer reviewed; Journal article, 2023)We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in ... 
Serre's Conjecture: Finitely generated projective modules over polynomial rings
Sandbakk, Fredrik (Master thesis, 2013)We start by proving that all finitely generated projective Rmodules, where R=k[x(1),...,x(n)] and k is a field, are stably free. Then we show that all stably free projective modules over a ring with the unimodular column ... 
Subcategory Classifications in Tensor Triangulated Categories
Sigstad, Henrik (Master thesis, 2011)It is known that the thick tensorideal subcategories in a tensor triangulated category can be classified via its prime ideal spectrum.We use this to provide new proofs of two wellknown classifications theorems:that of ... 
Subcategory structures, Grothendieck groups and higher homological algebra
Haugland, Johanne (Doctoral theses at NTNU;2023:113, Doctoral thesis, 2023) 
Support varieties for finite tensor categories: Complexity, realization, and connectedness
Bergh, Petter Andreas; Plavnik, Julia Yael; Witherspoon, Sarah (Journal article; Peer reviewed, 2021)We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the ... 
The Fundamental Group of SO(3)
Mork, Eirik Andreas (Master thesis, 2014)We study fundamental groups of topological spaces. In particular we will compute the fundamental group of SO(3), the group of rotations in three dimensions, by studying covering spaces. We will see that the fundamental ... 
The Homotopy Theory of (∞,1)Categories
HellstrømFinnsen, Magnus (Master thesis, 2014)The homotopy category of a stable (∞,1)category can be endowed with a triangulated structure. The main objective of this thesis is to give a proof of this fact. First it will be discussed some ideas of higher category ... 
Totally Acyclic Approximations
Bergh, Petter Andreas; Jorgensen, David A.; Moore, W. Frank (Journal article; Peer reviewed, 2021)Let Q→R be a surjective homomorphism of Noetherian rings such that Q is Gorenstein and R as a Qbimodule admits a finite resolution by modules which are projective on both sides. We define an adjoint pair of functors between ... 
Triangulated Categories and Matrix Factorizations
Langfeldt, Marit Buset (Master thesis, 2016)In this thesis we study triangulated categories and look at one specific example, the homotopy category of matrix factorizations. First we define categories and functors. Then we introduce additive and triangulated categories ... 
Ultraprodukter og anvendelser i kommutativ algebra
Kleven, John Aslak Wee (Bachelor thesis, 2024)Denne oppgaven gir en introduksjon til ultraprodukter, med sikte for å gjøre algebra med dem. Ultraproduktet, en konstruksjon fra modellteorien, er et slags gjennomsnitt av objektene det tar inn: Et ultraprodukt av ringer ... 
Unique factorization in Dedekind domains
Engdal, Simen Einmo (Master thesis, 2016)In this thesis we study ideals in Dedekind domains, which factorize uniquely into a product of prime ideals. As not every Dedekind domain is a unique factorization domain, a general element in these domains does not ... 
Unique Factorization of Ideals
Vold, Eirik Holteberg (Master thesis, 2013)We study Dedekind domains, where ideals factorize uniquely into a product ofprime ideals. This subject is of interest as general elements in these rings donot necessarily factorize uniquely.