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Rigidity in equivariant algebraicK-theory
等变代数理论中的刚性
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 ...
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    Functorality of the gamma filtration and computations for some twisted flag varieties
    gamma滤波的函数性及某些扭曲旗型的计算
    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 ...
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      Hausdorffified algebraic K1-groups andinvariants for C∗-algebras with the ideal property
      理想性质C*代数的hausdorfified代数K1群与变元
      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 ...
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        On refined metric and hermitian structures inarithmetic, I : Galois–Gauss sums and weak ramification
        关于精细度量与hermitian结构的拟合成，I:Galois-Gauss和与弱分支
        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...
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          Twisted iterated algebraic K-theory andtopological T-duality for sphere bundles
          扭曲迭代代数K-理论与球丛的拓扑T-对偶
          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...
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            Regularity estimates for elliptic nonlocal operators
            椭圆非局部算子的正则性估计
            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...
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              On the Hölder continuous subsolution problemfor the complex Monge–Ampère equation, II
              关于复Monge-Ampère方程的Hèlder连续亚解问题，II
              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...
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                Sharp Strichartz inequalities for fractional andhigher-order Schrödinger equations
                分数阶和高阶薛定谔方程的Sharp-Strichartz不等式
                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...
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                  The Calderón problem for the fractionalSchrödinger equation
                  分馏schródinger方程的Calderón问题
                  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...
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                    Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
                    流形上波动方程的变系数Wolff型不等式及sharp局部光滑估计
                    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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