Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The notion of space in Grothendieck: from schemes to a geometry of forms   In this essay we give a general picture about the evolution of Grohendieck's
ideas regarding the notion of space. Starting with his fundamental work in
algebraic geometry, where he introduces schemes and toposes as generalizations
of classical notions of spaces, passing through tame topology and ending with
the formulation of a geometry of forms, we show how the ideas of Grothendieck
evolved from pure mathematical considerations to physical and philosophical
questions about the nature and structure of space and its mathematical models.

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The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: econ