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Inter-universal geometry と ABC予想 (応援スレ) 77

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>>625
> つづき
> 
> In the case of the geometric Langlands conjecture, the proposed one-to-one correspondence is between two very different sets of objects, analogous to these spectrums and waves: on the spectrum side are abstract algebraic objects called representations of the fundamental group, which capture information about the kinds of loop that can wrap around certain complex surfaces; on the “wave” side are sheaves, which, loosely speaking, are rules assigning vector spaces to points on a surface. Gaitsgory has dedicated much of the last 30 years to the geometric Langlands conjecture. In 2013 he wrote an outline of the steps required for a proof, and after more than a decade of intensive research in 2024 he and his colleagues published the full proof, comprising over 800 pages spread over 5 papers. This is a monumental advance, expected to have deep implications in other areas of mathematics too, including number theory, algebraic geometry and mathematical physics.
> 
> 2025 New Horizons in Mathematics Prize
> Sam Raskin, Yale University
> For contributions to the geometric Langlands program, including the theory of the Whittaker model and the proof of the geometric Langlands conjecture in characteristic 0.
> 
> https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
> Proof of the geometric Langlands conjecture
> This page contains five papers, the combined content of which constitutes the proof of the (categorical, unramified) geometric Langlands conjecture.
> This is a collaborative project of D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum.
> Papers:
> GLC I: Construction of the functor
> GLC II: Kac-Moody localization and the FLE
> GLC III: Compatibility with parabolic induction
> GLC IV: Ambidexterity
> GLC V: The multiplicity one theorem
> (引用終り)
> 以上

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