arXiv subjects

Elías Guisado Villalgordo

Publications and source records attributed to Elías Guisado Villalgordo.

2 recordsLinked to original sources

arXiv2026

Fourier--Mukai loci are open and base change

We develop a theory of relative (quasi-)perfect complexes for algebraic spaces. Our main result proves that for a pseudocoherent kernel relatively perfect over both factors, the loci where its fiberwise Fourier--Mukai transform is fully faithful or an equivalence are open. The kernel need not be perfect, and these loci commute with Noetherian base change. Moreover, we provide an explicit autoequivalence for elliptic fibrations, and establish that smoothness and Gorensteinness are derived invariants.

math.AG↗

arXiv2026

Fiberwise criteria for Fourier--Mukai equivalences

We study the behavior of integral transforms under base change. In particular, we establish a yoga of local algebra and fibers to test for derived equivalences or fully faithfulness via integral transforms. This generalizes a result of Orlov to singular varieties and strengthens several results in the literature by allowing arbitrary base fields. Additionally, it provides new insight into fibrations and their singularities in arithmetic settings (e.g.\ projective and flat schemes over a DVR).

math.AG↗