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Showing 1 to 18 of 18 for “"Algebraic K-theory"”.
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Arithmetic duality in algebraic K-theory
… a compactly-supported variant Kc(X) of the algebraic K-theory spectrum K(X), and establish the basic functoriality of Kc. Briefly, K, behaves as if it were dual to K. Then we give this duality some grounding: for every prime t invertible on X, we define a natural l-adic pairing between Kc(X) …
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A Postnikov tower for algebraic K-theory
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.
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The Lefschetz -Reidemeister Trace in Algebraic K -Theory
… under a map of spaces whose domain is the K-theory of a ring with a bimodule and whose range is the Hochschild homology of the ring with the bimodule. One also recovers the Lefschetz-Nielsen series of the self-map in a similar context. This point of view suggests a natural extension of the …
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Motivic symmetric ring spectrum representing algebraic K-theory
… that there is a motivic spectrum representing algebraic K-theory. We describe an equivalent spectrum that is also a symmetric ring spectrum. A coherence problem occurs when one verifies the symmetry. It is explained and solved by introducing a category of vector bundles with strictly associative …
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Spaces of diffeomorphisms and embeddings via algebraic K-theory
… and embeddings of high-dimensional manifolds via algebraic K-theory. In the first paper, presented in Chapter 1, we show that the mapping class group is not an h-cobordism invariant of high-dimensional manifolds by exhibiting h-cobordant manifolds whose mapping class groups have different …
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A motivic norm structure on equivariant algebraic K-theory
Equivariant motivic homotopy theory is a homotopy theory of schemes with algebraic group actions. This thesis is mainly divided into two parts. In the first part, we define four model categories of motivic spectra that present the $\infty$-category $\SH^G(S)$. We use the model categorical setup to …
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The algebraic K-theory of the chromatic filtration and the telescope conjecture
We develop tools for understanding the algebraic K-theory of categories such as those coming from the chromatic filtration of the stable homotopy category, and apply these tools to improve our understanding of the large scale structure of stable homotopy theory and understand Ravenel's telescope …
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A weighty theorem of the heart for the algebraic K-theory of higher categories
… of Waldhausen’s sphere theorem for the algebraic K-theory of higher categories. The algebraic K-theory of a stable [infinity symbol]-category with a bounded non-degenerate weight structure is proven to be equivalent to the algebraic K-theory of the heart of the weight structure. We …
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On the infinitesimal theory of Chow groups
The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure. Except for the case p=1, which yields an algebraic group, the Chow groups remain mysterious. This …
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Adams Operations and the Dennis Trace Map
For a commutative algebra A, the algebraic K-theory of A, K*(A), and the Hochschild homology of A, HH*(A), are graded rings, and the Dennis trace map D : K *(A) → HH*( A) is a graded ring map. Since Hochschild homology is a more user friendly theory than the algebraic K-theory, one would like …
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The Ro (S¹)-graded equivariant homotopy of THH(Fp)
… odd dimensional [alpha]. These groups arise in algebraic K-theory computations, and are particularly important to the understanding of the algebraic K-theory of non-regular schemes. We also study RO(S¹)-graded TR-theory as an RO(S¹)-graded Mackey functor. Using Lewis and Mandell's homological …
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An infinite loop space structure for K-theory of bimonoidal categories
… the authors introduce the notion of the K- theory of a bimonoidal category R, and show that it is equivalent to the algebraic K-theory space of the ring spectrum KR. In this thesis we show that K(R) is the group completion of the classifying space of the 2-category ModR of modules over R, …
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Scissors congruence and K-theory
… a version of classical scissors congruence theory from the perspective of algebraic K-theory. Classically, two polytopes in a manifold X are defined to be scissors congruent if they can be decomposed into finite sets of pairwise-congruent polytopes. We generalize this notion to an abstract …
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Automorphisms and symbols in K(,2)
"Much of the work in algebraic K-theory today is devoted to the search for ""motivic cohomology."" This hoped-for cohomology theory of algebraic geometry should be analogous to the known singular homology groups of topology. In this work we consider Goodwillie and Lichtenbaum's candidate for …
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Higher Scissors Congruence Groups of the Euclidean Plane
… groups are examples of computations in algebraic K-theory, which are known to be exceedingly difficult. In the Euclidean plane, I obtain a complete answer for the computation of an approximation of all higher scissors congruence groups, where that approximation is defined by permitting …
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Constructing K-theory spectra from algebraic structures with a class of acyclic objects
… ways to construct categories admitting an algebraic K-theory spectrum, focusing on categories that contain some flavor of underlying algebraic structure as well as relevant homotopical information. In Part I, published as [20], we show that under certain technical conditions, a cotorsion …
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cdh descent for homotopy Hermitian K-Theory of rings with involution
… then prove a periodicity theorem for Hermitian K-theory and use it to construct an E-infinity motivic ring spectrum representing homotopy Hermitian K-theory. From these results, we show that the representing spectrum is stable under base change, and cdh descent for homotopy Hermitian K-theory of …
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Stabilizing spectral functors of exact categories
This Dissertation was approved for publication on 2017-07-13 at 15:08.