Quadratic sheaves and self-linkage

模层的连结

Linkage of sheaves of modules

受模连结理论启发，本文将连结概念推广至模层，证明了连结模层的局部性质及极大连结子模层的存在性。

模的链结层

Linked sheaves of modules

本文引入连通Noetherian概形上模层的链结概念，通过转置和合冲函子定义稳定层的链结，证明其局部性质及在仿射概形上等价于全局截面模的链结，并给出限制、粘合及非整环情形下的存在性判据，在射影情形比较了链结层的不变量。

Types of Linkage of Quadratic Pfister Forms

Given a field $F$ of positive characteristic $p$, $θ\in H_p^{n-1}(F)$ and $β,γ\in F^\times$, we prove that if the symbols $θ\wedge \frac{d β}β$ and $θ\wedge \frac{d γ}γ$ in $H_p^n(F)$ share the same factors in $H_p^1(F)$ then the symbol $θ\wedge \frac{d β}β \wedge \frac{d γ}γ$ in $H_p^{n+1}(F)$ is trivial. We conclude that when $p=2$, every two totally separably $(n-1)$-linked $n$-fold quadratic Pfister forms are inseparably $(n-1)$-linked. We also describe how to construct non-isomorphic $n$-fold Pfister forms which are totally separably (or inseparably) $(n-1)$-linked, i.e. share all common …

Smith-Treumann theory and the linkage principle

We apply Treumann's "Smith theory for sheaves" in the context of the Iwahori--Whittaker model of the Satake category. We deduce two results in the representation theory of reductive algebraic groups over fields of positive characteristic: (a) a geometric proof of the linkage principle; (b) a character formula for tilting modules in terms of the $\ell$-canonical basis, valid in all blocks and in all characteristics.

偶联类

Even Linkage Classes

本文将Martin-Deschamps和Perrin的$\E$和$\N$型分解推广到射影空间中纯余维的子概型，并证明了在简单的连接下，这些分解可通过映射锥过程互换.通过这些分解，Rao的对应被推广到给出了纯余维2的子概型的偶连接类与满足$H^1_*(\E)=0$和$\ext^1(\E^\vee, Ø)=0$的自反层$\E$的稳定等价类之间的一个双射.进一步地，这些决议被用来扩展马丁-德尚和Perrin的工作的Cohen-Macaulay曲线在$\Pthree$中的纯余维2的子计划在$\Pn$。特别是，甚至链接类这样的子计划有Lazarslog-Rao属性和任何最小的子计划，甚至链接类是直接链接到一个最小的子计划的对偶类。

On quadratic distinction of automorphic sheaves

We prove a geometric version of a classical result on the characterization of an irreducible cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_E)$ being the base change of a stable cuspidal packet of the quasi-split unitary group associated to the quadratic extension $E/F$, via the nonvanishing of certain period integrals, called being distinguished. We show that certain cohomology of an automorphic sheaf of $\mathrm{GL}_{n,X'}$ is nonvanishing if and only if the corresponding local system $E$ on $X'$ is conjugate self-dual with respect to an étale double cover $X'/X$ of curves,…