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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KAHW02 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

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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