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Article . 2025
License: CC BY
Data sources: Datacite
ZENODO
Article . 2025
License: CC BY
Data sources: Datacite
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On a Newfound Panorama in Geometry and Category Theory: A Tribute to Grothendieck

Authors: de ceuster, peter;

On a Newfound Panorama in Geometry and Category Theory: A Tribute to Grothendieck

Abstract

 This paper revisits the foundational landscapes introduced by Alexander Grothendieck—topos theory, motives, schemes, and the universal language of categories—through the lens of twenty-first-century advances. We explore how concepts such as ∞-categories, derived algebraic geometry, homotopy type theory, and arithmetic mirror symmetry do not merely extend, but profoundly reframe and realize Grothendieck’s unifying vision. By synthesizing these modern perspectives, we aim to demonstrate that the seeds planted in his monumental works, from EGA and SGA to the philosophical reflections in Récoltes et Semailles, have grown into a vast, interconnected panorama. Emphasizing this ethos of unity, we propose a novel framework of ’Spectral Grothendieck Spaces’ as a potential arena for future unification, encoding classical schemes, derived stacks, motivic towers, and logical universes within a single, cohesive structure.

Keywords

schemes, topos, grothendieck

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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