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作者:Niko Naumann , Charanya Ravi
来源:[J].Annals of K-Theory, 2020, Vol.5 (1), pp.141-158
摘要:If $(R,I)$ is a henselian pair with an action of a finite group$G$ and $n\ge 1$ is an integer coprime to $|G|$ such that $n\cdot |G|\inR^*$, then the reduction map of mod-$n$equivariant $K\mkern-2mu$-theory spectra\[K^G(R)/n\xrightarrow{\simeq\,}K^G(R/I)/n\]is an equivalence. We ...
作者:Eoin Mackall
来源:[J].Annals of K-Theory, 2020, Vol.5 (1), pp.159-180
摘要:We introduce techniques for uniformly studying the gamma filtration ofprojective homogeneous varieties. These techniques are utilized in some casesof inner-twisted flag varieties (of type A) to show that functorality knownfor the Chow rings of these varieties also extends to the ...
作者:Guihua Gong , Chunlan Jiang , Liangqing Li
来源:[J].Annals of K-Theory, 2020, Vol.5 (1), pp.43-78
摘要:A $C^*$-algebra $A$ is said to have the ideal property if each closedtwo-sided ideal of $A$ is generatedas a closed two-sided ideal by the projections inside theideal. $C^*$-algebras with the ideal property are ageneralization and unification of real rank zero $C^*$-algebras and ...
作者:Werner Bley , David Burns , Carl Hahn
来源:[J].Annals of K-Theory, 2020, Vol.5 (1), pp.79-140
摘要:\advance\leftskip by-1pt\advance\rightskip by-1ptWe use techniques of relative algebraic $K$-theory todevelop a common refinement of the theories of metrized and hermitian Galoisstructures in arithmetic. As a first application of the general approach,we then use it to prove sever...
作者:John Lind , Hisham Sati , Craig Westerland
来源:[J].Annals of K-Theory, 2020, Vol.5 (1), pp.1-42
摘要:We introduce a periodic form of the iterated algebraic$K$-theory of $ku$, the (connective) complex $K$-theory spectrum, as well as anatural twisting of this cohomology theory by higher gerbes. Furthermore,we prove a form of topological T-duality for sphere bundles oriented withre...
作者:Bartłomiej Dyda , Moritz Kassmann
来源:[J].Analysis & PDE, 2020, Vol.13 (2), pp.317-370
摘要:We study weak solutions to nonlocal equations governed by integrodifferentialoperators. Solutions are defined with thehelp of symmetric nonlocal bilinear forms. Throughout thiswork, our main emphasis is onoperators with general, possibly singular, measurable kernels. We obtainreg...
作者:Ngoc Cuong Nguyen
来源:[J].Analysis & PDE, 2020, Vol.13 (2), pp.435-453
摘要:We solve the Dirichlet problem for the complex Monge--Amp\`ereequation on a strictly pseudoconvex domain with the right-hand side beinga positive Borel measure which is dominated by the Monge--Amp\`ere measureof a H\"older continuous plurisubharmonic function. If the boundary dat...
作者:Gianmarco Brocchi , Diogo Oliveira e Silva , René Quilodrán
来源:[J].Analysis & PDE, 2020, Vol.13 (2), pp.477-526
摘要:We investigate a class of sharp Fourier extension inequalities on the planarcurves $s=|y|^p\mkern-2mu$,\, $p>1$.We identify the mechanism responsible for the possible loss of compactnessof nonnegative extremizing sequences, and prove that extremizers exist if$14$.In particular, t...
作者:Tuhin Ghosh , Mikko Salo , Gunther Uhlmann
来源:[J].Analysis & PDE, 2020, Vol.13 (2), pp.455-475
摘要:We show global uniqueness in an inverse problem for the fractionalSchr\"odinger equation: an unknown potential in a bounded domain isuniquely determined by exterior measurements of solutions. We also showglobal uniqueness in the partial data problem where measurements are takenin...
作者:David Beltran , Jonathan Hickman , Christopher D. Sogge
来源:[J].Analysis & PDE, 2020, Vol.13 (2), pp.403-433
摘要:The sharp Wolff-type decoupling estimates of Bourgain and Demeter are extendedto the variablecoefficient setting. These results are applied to obtain newsharp local smoothing estimates for wave equations on compact Riemannianmanifolds, away from the endpoint regularity exponent. ...

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