UC Santa Cruz

This thesis explores the tensor triangular classification of pseudo-coherent complexes over a commutative noetherian ring with particular emphasis on the case of a discrete valuation ring. In the latter case, we derive key connections between thick tensor-ideals of pseudo-coherent complexes and the asymptotic behavior of torsion degree sequences. This leads to a description of the Balmer spectrum of the derived category of pseudo-coherent complexes as the spectral space associated via Stone duality with a certain lattice of asymptotic equivalence classes of monotonic sequences of natural numbers. We also generalize some of these results from discrete valuation rings to the ring of integers.