• Corpus ID: 239050209

Almost coherent modules and almost coherent sheaves

@inproceedings{Zavyalov2021AlmostCM,
  title={Almost coherent modules and almost coherent sheaves},
  author={Bogdan Zavyalov},
  year={2021}
}
We review the theory of almost coherent modules that was introduced in"Almost Ring Theory"by Gabber and Ramero. Then we globalize it by developing a new theory of almost coherent sheaves on schemes and on a class of"nice"formal schemes. We show that these sheaves satisfy many properties similar to usual coherent sheaves, i.e. the Almost Proper Mapping Theorem, the Formal GAGA, etc. We also construct an almost version of the Grothendieck twisted image functor $f^!$ and verify its properties… 
2 Citations
Moduli spaces in $p$-adic non-abelian Hodge theory
We propose a new moduli theoretic approach to the p-adic Simpson correspondence for a smooth proper rigid space X with coefficients in any rigid analytic group G, in terms of a comparison of moduli
$G$-torsors on perfectoid spaces
For any rigid analytic group variety G over a non-archimedean field K over Q p , we study G -torsors on adic spaces over K in the v -topology. Our main result is that on perfectoid spaces, G -torsors