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https://gnanaganga.inflibnet.ac.in:8443/jspui/handle/123456789/6360
Title: | The Homotopy Obstructions in Complete Intersections |
Authors: | Satya Mandal Bibekananda Mishra |
Issue Date: | 2019 |
Publisher: | Journal of the Ramanujan Mathematical Society |
Abstract: | Let A be a regular ring over a field k, with 1/2 Є k, and dim A = d. We discuss the Homotopy Obstruction Program, in the complete intersection case. Fix an integer n ≥ 2. A local orientation is a pair (I,ω), where I is an ideal and ω - A^n ↠ I/I^2 is a surjective map. The goal is to define and detect homotopy obstructions, for ω to lift to a surjective map A^n ↠ I . Denote the set of all local orientations by LO(A, n). A homotopy relations on LO(A, n) is induced by the maps LO(A, n)←T=0 LO(A[T ], n) →T=1 LO(A, n). The homotopy obstruction set π0(LO(A, n)) is defined to be the set of all equivalence classes. Assume 2n ≥d+2. We prove that π0(LO(A, n)) is an abelian group. We also establish a surjective map ρ - E^n(A)a↠ π0(LO(A, n)), where E^n(A) denotes the Euler class group. When 2n ≥ d + 3, and A is essentially smooth, we prove ρ is an isomorphism. This settles a conjecture of Morel. |
URI: | http://gnanaganga.inflibnet.ac.in:8080/jspui/handle/123456789/6360 |
Appears in Collections: | Articles to be qced |
Files in This Item:
File | Size | Format | |
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The Homotopy obstructions in complete intersections.pdf Restricted Access | 1.17 MB | Adobe PDF | View/Open Request a copy |
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