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A Baum–Connes conjecture for singularfoliations
作者：Iakovos Androulidakis , Georges Skandalis
来源：[J].Annals of K-Theory, 2020, Vol.4 (4), pp.561-620MSP
摘要：We consider singular foliations whose holonomy groupoid may be nicelydecomposed using Lie groupoids (of unequal dimension). We construct a$K\mkern-2mu$-theory group and a natural assembly type morphism to the $K\mkern-2mu$-theory ofthe foliation $C^*$-algebra generalizing to the ...
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    A generalized Vaserstein symbol
    作者：Tariq Syed
    来源：[J].Annals of K-Theory, 2020, Vol.4 (4), pp.671-706MSP
    摘要：Let $R$ be a commutative ring. For any projective $R$-module $P_0$ of constantrank $2$ with a trivialization of its determinant, we define a generalizedVaserstein symbol on the orbit space of the set of epimorphisms $P_0 \oplusR \rightarrow R$ under the action of the group of ele...
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      A Dolbeault–Hilbert complex for a variety withisolated singular points
      作者：John Lott
      来源：[J].Annals of K-Theory, 2020, Vol.4 (4), pp.707-720MSP
      摘要：Given a compact Hermitian complex space with isolated singular points,we construct a Dolbeault-type Hilbert complex whose cohomology is isomorphicto the cohomology of the structure sheaf. We show that thecorrespondingK-homologyclass coincides with the one constructed byBaum, Fult...
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        Witt groups of abelian categories and perverse sheaves
        作者：Jörg Schürmann , Jonathan Woolf
        来源：[J].Annals of K-Theory, 2020, Vol.4 (4), pp.621-670MSP
        摘要：We study the Witt groups $W_{\pm}(\operatorname{Perv}{X})$ of perversesheaves on a finite-dimensionaltopologically stratified space $X$ witheven-dimensional strata.We show that $W_{\pm}(\operatorname{Perv}{X})$ has a canonical decomposition as a directsum of the Witt groups of sh...
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          On the intersection motive of certain Shimura varieties: the case of Siegel threefolds
          作者：Jörg Wildeshaus
          来源：[J].Annals of K-Theory, 2020, Vol.4 (4), pp.525-559MSP
          摘要：We construct a Hecke-equivariant Chow motive whoserealizations equalintersection cohomology of Siegelthreefolds with regular algebraic coefficients.As a consequence, we are able to define Grothendieck motivesfor Siegel modular forms.
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            Moments of random multiplicative functions, II: High moments
            作者：Adam J Harper
            来源：[J].Algebra & Number Theory(IF 0.625), 2020, Vol.13 (10), pp.2277-2321MSP
            摘要：We determine the order of magnitude of $\mathbb{E}\bigl \lvert \sum_{n \leq x} f(n)\bigr \rvert ^{2q}$up to factors of size $e^{O(q^2)}$, where $f(n)$ is a Steinhaus orRademacher random multiplicative function, for all real $1 \leq q\leq c\log x / \log\log x$.In the Steinhaus cas...
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              Combinatorial identities and Titchmarsh’sdivisor problem for multiplicative functions
              作者：Sary Drappeau , Berke Topacogullari
              来源：[J].Algebra & Number Theory(IF 0.625), 2020, Vol.13 (10), pp.2383-2425MSP
              摘要：Given a multiplicative function $f$ which is periodic over theprimes, we obtain a full asymptotic expansion for the shiftedconvolution sum $\sum_{\lvert h\rvert ...
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                The construction problem for Hodge numbers modulo an integer
                作者：Matthias Paulsen , Stefan Schreieder
                来源：[J].Algebra & Number Theory(IF 0.625), 2020, Vol.13 (10), pp.2427-2434MSP
                摘要：For any integer $m\ge2$ and any dimension $n\ge1$, we show that any$n$-dimensional Hodge diamond with values in $\mathbb{Z}/m\mathbb{Z}$is attained by the Hodge numbers of an $n$-dimensional smooth complexprojective variety.As a corollary, there are no polynomial relations among ...
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                  A well-posedness result for viscous compressible fluids with only bounded density
                  作者：Raphaël Danchin , Francesco Fanelli , Marius Paicu
                  来源：[J].Analysis & PDE, 2020, Vol.13 (1), pp.275-316MSP
                  摘要：We are concerned with the existence and uniqueness of solutions withonly boundeddensity for the barotropic compressible Navier--Stokes equations.Assuming that the initial velocity has slightly subcritical regularityand that the initial density is a small perturbation (in the $L^\...
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                    Infinite-time blow-up for the 3-dimensional energy-critical heat equation
                    作者：Manuel del Pino , Monica Musso , Juncheng Wei
                    来源：[J].Analysis & PDE, 2020, Vol.13 (1), pp.215-274MSP
                    摘要：\advance\leftskip-3pt\advance\rightskip-3ptWe construct globally defined in time, unbounded positive solutions tothe energy-critical heat equation in dimension~3\[u_t = \Delta u + u^5 \quad \text{in } \mathbb{R}^3 \times (0,\infty),\qquad u(x, 0)= u_0 (x)\quad\text{in } \mathbb{R...
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