Reduced Tate-Shafarevich group
Abstract
We prove a sort of reconstruction theorem for generic elliptic Calabi-Yau -folds in the sense of C\u{a}ld\u{a}raru. From our argument it follows that two generic elliptic Calabi-Yau -folds are derived-equivalent linear over the base if and only if their generic fibers are derived-equivalent. As an application, we give affirmative answers to the conjectures raised by Knapp-Scheidegger-Schimannek. Namely, for each pair of elliptic Calabi-Yau -folds in their list we prove that they share the relative Jacobian and are -linear derived-equivalent.
Keywords
Cite
@article{arxiv.2205.11268,
title = {Reduced Tate-Shafarevich group},
author = {Hayato Morimura},
journal= {arXiv preprint arXiv:2205.11268},
year = {2024}
}
Comments
22 pages; v3: Removed results about nonbirationality and computation of Tate--Shafarevich group. Modified a statement and the proofs in the subsection Calabi--Yau case. Added sections corresponding to arXiv:2301.12751v4 after some modifications