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Cohomology of quasi-coherent modules
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The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary
We give two proofs that appropriately defined congruence subgroups of the map** class group of a surface with punctures/boundary have enormous...
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On Yuzvinsky’s lattice sheaf cohomology for hyperplane arrangements
We establish the relationship between the cohomology of a certain sheaf on the intersection lattice of a hyperplane arrangement introduced by...
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Relative cohomology of Dolbeault modules
In this chapter, K denotes a complete discrete valuation field of characteristic 0, with algebraically closed residue field k of characteristic p >...
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Hodge cohomology with a ramification filtration, I
We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors “at infinity”. We show that the...
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Continuous K-theory and cohomology of rigid spaces
We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete...
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Étale cohomology of algebraizable rigid analytic varieties via nearby cycles over general bases
We prove a finiteness theorem and a comparison theorem in the theory of étale cohomology of rigid analytic varieties. By a result of Huber, for a...
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Combinatorial and topological aspects of path posets, and multipath cohomology
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate...
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Homology II: Cohomology to Ranking Problems
In this chapter we introduce cohomology; the constructions have roots in topology and geometry, and as such, can come with extra structure. We begin...
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Reconstruction of the stacky approach to de Rham cohomology
In this short paper, we use Tannakian reconstruction techniques to prove a result that explains how to reconstruct the stacky approach to de Rham...
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Finiteness of Cohomology for Pro-locally Proper Maps
We introduce a notion of proper morphism for schematic finite spaces and prove the analog of Grothendieck’s finiteness theorem for it. The techniques...
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The Moduli Space of Stable Coherent Sheaves via Non-archimedean Geometry
We provide a construction of the moduli space of stable coherent sheaves in the world of non-archimedean geometry, where we use the notion of...
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Cohomology of projective and proper schemes
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