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 ...
 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...
 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...
 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...
 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.
 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...
 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 $\sum_{\lvert h\rvert ...  作者：Matthias Paulsen , Stefan Schreieder 来源：[J].Algebra & Number Theory(IF 0.625), 2020, Vol.13 (10), pp.2427-2434MSP 摘要：For any integer$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$-dimensional smooth complexprojective variety.As a corollary, there are no polynomial relations among ...  作者：Raphaël Danchin , Francesco Fanelli , Marius Paicu 来源：[J].Analysis & PDE, 2020, Vol.13 (1), pp.275-316MSP 摘要：We are concerned with the existence and uniqueness of solutions withonly boundeddensity for the barotropic compressible Navier--Stokes equations.Assuming that the initial velocity has slightly subcritical regularityand that the initial density is a small perturbation (in the$L^\...
 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...