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17
Localization theorems in topological Hochschild homology and topological cyclic homology
, 2008
"... We construct localization cofiber sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of spectral categories. Using a “global ” construction of the THH and TC of a scheme in terms of the perfect complexes in a spectrally enriched version of the category of ..."
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Cited by 48 (8 self)
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We construct localization cofiber sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of spectral categories. Using a “global ” construction of the THH and TC of a scheme in terms of the perfect complexes in a spectrally enriched version of the category of unbounded complexes, the sequences specialize to localization cofiber sequences associated to the inclusion of an open subscheme. These are the targets of the cyclotomic trace from the localization sequence of ThomasonTrobaugh in Ktheory. We also deduce versions of Thomason’s blowup formula and the projective bundle formula for THH and TC.
A curious example of triangulatedequivalent model categories which are not Quillen equivalent
 GEOM. TOPOL
, 2009
"... The paper gives a new proof that the model categories of stable modules for the rings Z=p 2 and Z=pŒ =. 2 / are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose ..."
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Cited by 4 (0 self)
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The paper gives a new proof that the model categories of stable modules for the rings Z=p 2 and Z=pŒ =. 2 / are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with nonisomorphic K–theories.
Classifying Rational GSpectra for Finite G
, 2008
"... We give a new proof that for a finite group G, the category of rational Gequivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. F ..."
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Cited by 4 (3 self)
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We give a new proof that for a finite group G, the category of rational Gequivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. Furthermore the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model. 1
A curious example of two model categories and some associated differential graded algebras, in preparation
"... Abstract. The paper gives a new proof that the model categories of stable modules for the rings Z/p 2 and Z/p[ɛ]/(ɛ 2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent ..."
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Cited by 2 (1 self)
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Abstract. The paper gives a new proof that the model categories of stable modules for the rings Z/p 2 and Z/p[ɛ]/(ɛ 2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with nonisomorphic Ktheories. Contents
Homotopy theory of Gdiagrams and equivariant excision, preprint available at math.AT/1403.6101
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The Higher RiemannHilbert Correspondence and Multiholomorphic Mappings
, 2011
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speaks to graduates
, 1940
"... This accomplishment –no matter how grand or how modest – could not have been reached without the support of many individuals who formed an important part of my life –both mathematical and otherwise. The most immediate thanks go out to Jonathan Block, my advisor, who gently pushed me towards new math ..."
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Cited by 1 (0 self)
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This accomplishment –no matter how grand or how modest – could not have been reached without the support of many individuals who formed an important part of my life –both mathematical and otherwise. The most immediate thanks go out to Jonathan Block, my advisor, who gently pushed me towards new mathematical ventures and whose generosity and patience gave me some needed workingspace. He shared his insights and knowledge freely, and gave me a clear picture of an ideal career as a mathematician. I must also thank him for his warm hospitality, and introducing me to his family. I am also gracious for the presence of Tony Pantev, who was a kind of advisorfromafar during my tenure, and whose students were often my secondary mathematical mentors. Collectively that are responsible for a significant amount of learning on my part. I also