16 research outputs found

    On Kato and Kuzumaki's properties for the Milnor K2K_2 of function fields of pp-adic curves

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    Let KK be the function field of a curve CC over a pp-adic field kk. We prove that, for each n,d≥1n, d \geq 1 and for each hypersurface ZZ in PKn\mathbb{P}^n_{K} of degree dd with d2≤nd^2 \leq n, the second Milnor KK-theory group of KK is spanned by the images of the norms coming from finite extensions LL of KK over which ZZ has a rational point. When the curve CC has a point in the maximal unramified extension of kk, we generalize this result to hypersurfaces ZZ in PKn\mathbb{P}^n_{K} of degree dd with d≤nd \leq n.Comment: 34 pages. Final versio

    Geometrical and inertial properties of a class of thin shells of a general type

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    IBM 7094 Fortran program for evaluating surface area, centroids of surface volume or masses, and moments of inertia for thin walled shell

    Equivariant AA-theory

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    We give a new construction of the equivariant KK-theory of group actions [\textit{C. Barwick}, "Spectral Mackey functors and equivariant algebraic -theory (I)", Adv. Math. 304, 646-727 (2017; Zbl 1348.18020) and \textit{C. Barwick} et al., "Spectral Mackey functors and equivariant algebraic -theory (II)", Preprint (2015); \url{arXiv:1505.03098}], producing an infinite loop GG-space for each Waldhausen category with GG-action, for a finite group GG. On the category R(X)R(X) of retractive spaces over a GG-space XX, this produces an equivariant lift of Waldhausen's functor A(X)A(X), and we show that the HH-fixed points are the bivariant AA-theory of the fibration XhH→BHX_{hH}\to BH. We then use the framework of spectral Mackey functors to produce a second equivariant refinement AG(X)A_G(X) whose fixed points have tom Dieck type splittings. We expect this second definition to be suitable for an equivariant generalization of the parametrized hh-cobordism theorem

    The Independent, V. 75, Thursday, February 2, 1950, [Number: 36]

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    [6] p. Newspaper published in Collegeville, Pa. Weekly. Contains local, county, state and national news, agricultural reading matter, fiction, public sales and advertisements.https://digitalcommons.ursinus.edu/independent/3647/thumbnail.jp
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