Framed motives of smooth affine pairs |
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Authors: | A Druzhinin |
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Institution: | 1. Universidad de Cádiz, Puerto Real, Cádiz, Spain;2. CMCC, Universidade Federal do ABC, Santo André, Brazil;3. CMUP, Faculdade de Ciências, Universidade do Porto, Porto, Portugal;4. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia;5. Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, Brazil;6. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal;7. Saint Petersburg University, Saint Petersburg, Russia;1. Utah State University, Department of Mathematics and Statistics, Logan UT 84341, USA;2. Hung Vuong University, Faculty of Natural Sciences, Viet Tri, Phu Tho, Viet Nam;3. Université Bretagne Sud, Laboratoire de Mathématiques de Bretagne Atlantique, UMR CNRS 6205, Campus de Tohannic, BP 573 F-56017 Vannes, France;1. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India;2. Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, 502285, Telangana, India;1. Department of Mathematics, University of Western Ontario, London, Ontario, Canada;2. Department of Mathematics, University of Ljubljana, Jadranska Ulica 21, 1000 Ljubljana, Slovenia;1. Tulane University, Department of Mathematics, 6823 St. Charles Ave., New Orleans, LA 70118, USA;2. Department of Mathematics, University of Nebraska – Lincoln, Lincoln, NE 68588, USA;3. University of Education, Hue University, 34 Le Loi St., Hue, Viet Nam |
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Abstract: | The theory of framed motives by Garkusha and Panin gives computations in the stable motivic homotopy category in terms of Voevodsky's framed correspondences. In particular, the motivically fibrant Ω-resolution in positive degrees of the motivic suspension spectrum , where , for a smooth scheme over an infinite perfect field k, is computed.The computation by Garkusha, Neshitov and Panin of the framed motives of relative motivic spheres , , is one of ingredients in the theory. In the article we extend this result to the case of a pair given by a smooth affine variety X over k and an open subscheme .The result gives an explicit motivically fibrant Ω-resolution in positive degrees for the motivic suspension spectrum of the quotient-sheaf . |
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Keywords: | Stable motivic homotopy theory Fibrant resolutions Framed motives Moving lemmas |
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