We formulate the geometric P=W conjecture for singular character varieties. We establish it for compact Riemann surfaces of genus one, and obtain partial results in arbitrary genus. To this end, we employ non-Archimedean, birational and degeneration techniques to study the topology of the dual boundary complex of certain character varieties. We also clarify the relation between the geometric and the cohomological P=W conjectures.Comment: 33 pages. New appendix. Other minor changes. Final version in Selecta Mathematic
We prove a general finiteness statement for the ordered abelian group of tropical functions on skele...
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called ...
We establish P=W and PI=WI conjectures for character varieties with structural group $\mathrm{GL}_n$...
We formulate the geometric P=W conjecture for singular character varieties. We establish it for comp...
We associate a weight function to pairs consisting of a smooth and proper variety X over a complete ...
This thesis applies the techniques of non-archimedean geometry to the study of degenerations and com...
In view of the recent proofs of the $P=W$ conjecture, the present paper reviews and relate the lates...
In this thesis we examine some aspects of the topology of dual complexes under three different view...
This thesis examines the nature of Temkin’s canonical metrics on the sheaves of differentials of Ber...
This thesis examines the nature of Temkin’s canonical metrics on the sheaves of differentials of Ber...
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincar\'e ...
We consider an algebraic variety X together with the choice of a subvariety Z. We show that any cohe...
In this paper we determine the motivic class--in particular, the weight polynomial and conjecturally...
We prove invariance results for the cohomology groups of ideal sheaves of simple normal crossing div...
We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating ...
We prove a general finiteness statement for the ordered abelian group of tropical functions on skele...
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called ...
We establish P=W and PI=WI conjectures for character varieties with structural group $\mathrm{GL}_n$...
We formulate the geometric P=W conjecture for singular character varieties. We establish it for comp...
We associate a weight function to pairs consisting of a smooth and proper variety X over a complete ...
This thesis applies the techniques of non-archimedean geometry to the study of degenerations and com...
In view of the recent proofs of the $P=W$ conjecture, the present paper reviews and relate the lates...
In this thesis we examine some aspects of the topology of dual complexes under three different view...
This thesis examines the nature of Temkin’s canonical metrics on the sheaves of differentials of Ber...
This thesis examines the nature of Temkin’s canonical metrics on the sheaves of differentials of Ber...
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincar\'e ...
We consider an algebraic variety X together with the choice of a subvariety Z. We show that any cohe...
In this paper we determine the motivic class--in particular, the weight polynomial and conjecturally...
We prove invariance results for the cohomology groups of ideal sheaves of simple normal crossing div...
We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating ...
We prove a general finiteness statement for the ordered abelian group of tropical functions on skele...
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called ...
We establish P=W and PI=WI conjectures for character varieties with structural group $\mathrm{GL}_n$...
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