Canonical q
Related Concepts
Cohomology
Mathematics
Geometry
De Rham cohomology
Algebra over a field
Pure mathematics
Equivariant cohomology
Peter Scholze
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.5802/afst.1563
· OA: W2963832849
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.5802/afst.1563
· OA: W2963832849
In recent work with Bhatt and Morrow, we defined a new integral <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-adic cohomology theory interpolating between étale and de Rham cohomology. An unexpected feature of this cohomology is that in coordinates, it can be computed by a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-deformation of the de Rham complex, which is thus canonical, at least in the derived category. In this short survey, we try to explain what we know about this phenomenon, and what can be conjectured to hold.
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