Work

Tate modules as condensed modules

Year: 2026

Type: article

Abstract: We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free module of infinite countable rank under direct sums, duals and retracts. In the ‐categorical context, under the same assumption on the base ring, we establish a fully faithful embedding of the ‐category of countable Tate objects in perfect complexes, with uniformly bounded tor‐amplitude, into the derived ‐category of condensed modules. The boundedness assumption is necessary to ensure fullness, as we prove via an explicit counterexample in the unbounded case.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70418

Authors: Valerio Melani, Hugo Pourcelot, Gabriele Vezzosi

Institutions: University of Florence, Université d'Angers

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

OpenAlex ID: W4406785109

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