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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…
math.LO2023
Existential closedness of as a globally valued field via Arakelov geometry
Michał Szachniewicz
We use the differentiability of the arithmetic volume function and an arithmetic Bertini type theorem to classify when one can find a closed point on the generic fiber of an arithm…