University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > CANCELLED A1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections

CANCELLED A1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections

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We equate various Euler classes of algebraic vector bundles, including those of Barge—Morel, Kass—W., Déglise—Jin—Khan, and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of Scheja and Storch. As an application, we compute the Euler classes associated to arithmetic counts of d-planes on complete intersections in P^n in terms of topological Euler numbers over R and C. This is joint work with Tom Bachmann




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