与弗罗贝纽斯换向的傅立叶-穆凯变换

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-09-04 DOI:10.1112/blms.13145

Daniel Bragg

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摘要

我们证明，特性为 p $p$ 的光滑投影变种之间的傅立叶-穆凯等价关系，与沿弗罗贝纽斯的前推或后拉相通，是移位、同构和张量乘积与可逆剪切的组合，其 ( p - 1 ) $(p-1)$ th 张量幂是微不足道的。

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Fourier–Mukai transforms commuting with Frobenius

We show that a Fourier–Mukai equivalence between smooth projective varieties of characteristic $p$ that commutes with either pushforward or pullback along Frobenius is a composition of shifts, isomorphisms, and tensor products with invertible sheaves whose $(p - 1)$ th tensor power is trivial.