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Register a new userTHH and TC are (very) far from being homotopy functors
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Authors
Elden Elmanto
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We compute the $mathbb{A}^1$-localization of several invariants of schemes namely, topological Hochschild homology ($mathrm{THH}$), topological cyclic homology ($mathrm{TC}$) and topological periodic cyclic homology ($mathrm{TP}$). This procedure is quite brutal and kills the complete
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We equate various Euler classes of algebraic vector bundles, including those of [BM, KW, DJK], 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.
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