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math.NT2024
Continuity of heights in families and complete intersections in toric varieties
Pablo Destic, Nuno Hultberg, Michał Szachniewicz
We study the variation of heights of cycles in flat families over number fields or, more generally, globally valued fields. To a finite type scheme over a GVF we associate a locall…
math.LO2024
Globally valued fields: foundations
Itaï Ben Yaacov, Pablo Destic, Ehud Hrushovski +1
We present foundations for globally valued fields, a class of enriched fields capturing some aspects of the geometry of global fields, based on the product formula. We show that th…
math.LO2024
Hyperbolicity and model-complete fields
Michał Szachniewicz, Jinhe Ye
We study model-complete fields that avoid a given quasi-project variety . There is a close connection between hyperbolicity of and the existence of the model companion for t…