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Theses

Motivic Approach to Enumerating Vector Bundles

Abstract : In this thesis, we establish, via obstruction theory in motivic homotopy theory, some enumeration results on vector bundles of rank dover a smooth affine k-algebra A of dimension d for a base field k, in analogy with some results of James-Thomas. In the rank d case, we recover in particular results of Suslin and Bhatwadekar on cancellation of such vector bundles. Admitting a conjecture of Asok and Fasel, we prove cancellation of such modules of rank d-1 if the base field k is algebraically closed. Using similar methods, we also obtain cancellation results for symplectic vector bundles of critical rank.
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Peng Du. Motivic Approach to Enumerating Vector Bundles. K-Theory and Homology [math.KT]. Université Grenoble Alpes [2020-..], 2020. English. ⟨NNT : 2020GRALM021⟩. ⟨tel-03009926⟩

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