arXiv subjects

Aron Heleodoro

Publications and source records attributed to Aron Heleodoro.

4 recordsLinked to original sources

arXiv2023

On the normally ordered tensor product and duality for Tate objects

This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We list some applications: (1) Pontryagin duality uniquely extends to n-Tate objects in locally compact abelian groups; (2) Adeles of a flag can be written as ordered tensor products; (3) Intersection numbers can be interpreted via these tensor products.

math.QA↗

arXiv2022

A Remark on Lurie's Representability Theorem

In this note we revisit Lurie's representability theorem for geometric stacks and prove that one of the conditions can be mildly relaxed. The proof uses ideas from Hall--Rydh's work on the (classical) Artin's representability theorem. We also spell out a couple of variants of the main theorem and review the relation between deformation theory and homogeneity conditions on prestacks.

math.AG↗

arXiv2020

Prestacks of Tate type

This paper introduces the notion of prestacks of Tate type and studies natural geometric conditions on them. We also develop a formalism of Tate-coherent sheaves and define a dualizing gerbe for Tate schemes locally almost of finite type.

math.AG↗

arXiv2020

Determinant map for the prestack of Tate objects

We construct a map from the prestack of Tate objects over a commutative ring $k$ to the stack of $\mathbb{G}_{\rm m}$-gerbes. The result is obtained by combining the determinant map from the stack of perfect complexes as proposed by Schürg-Toën-Vezzosi with a relative $S_{\bullet}$-construction for Tate objects as studied by Braunling-Groechenig-Wolfson. Along the way we prove a result about the K-theory of vector bundles over a connective $\mathbb{E}_{\infty}$-ring spectrum which is possibly of independent interest.

math.AG↗