Related papers: On the p-adic weight-monodromy conjecture for comp…
We study the collection of measures obtained via push-forward along a map between smooth varieties over p-adic fields. We investigate when the stalks of this collection are finite-dimensional. We provide an algebro-geometric criterion…
We discuss an experimental approach to open problems in toric geometry: are smooth projective toric varieties (i) projectively normal and (ii) defined by degree 2 equations? We discuss the creation of lattice polytopes defining smooth toric…
We study ordinary abelian schemes in characteristic $p$ and their moduli spaces from the perspective of char $p$ Mumford--Tate, log Ax--Lindemann, and geometric Andr\'e--Oort conjectures (abbreviated as $\MTT_p$, $\mathrm{logAL}_p$ and…
We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties in any characteristic, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to…
We prove that $p$-adic geometric pro-\'etale cohomology of smooth partially proper rigid analytic varieties over $p$-adic fields seen in the category of Topological Vector Spaces satisfies a Poincar\'e duality as we have conjectured. This…
Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof…
We prove that the weight polytope of the Hurwitz form of a polarized smooth toric variety coincides with the convex hull of the characteristic vectors introduced in the previous work of Ogusu and the author with respect to all regular…
R.~Lawrence has conjectured that for rational homology spheres, the series of Ohtsuki's invariants converges p-adicly to the SO(3) Witten-Reshetikhin-Turaev invariant. We prove this conjecture for Seifert rational homology spheres. We also…
The purpose of this paper is to prove a basic $p$-adic comparison theorem for smooth rigid analytic and dagger varieties over the algebraic closure $C$ of a $p$-adic field: $p$-adic pro-\'etale cohomology, in a stable range, can be…
We study aspects related to Kontsevich's homological mirror symmetry conjecture in the case of Calabi-Yau complete intersections in toric varieties. In a 1996 lecture at Rutgers University, Kontsevich indicated how his proposal implies that…
We prove a combinatorial version of Thom's Isotopy Lemma for projection maps applied to any complex or real toric variety. Our results are constructive and give rise to a method for associating the Whitney strata of the projection to the…
We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after a finite \'etale cover, admit a toric fibration over…
We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce…
By using the equivariant localization formula of toric varieties. We prove the vanishing of the Witten genus of some string complete intersections in smooth toric varieties.
We prove two conjectures on weighted complete intersections and give the complete classification of threefold weighted complete intersections in weighted projective space that are canonically or anticanonically embedded.
We compute, in a stable range, the arithmetic p-adic etale cohomology of smooth rigid analytic and dagger varieties (without any assumption on the existence of a nice integral model) in terms of differential forms using syntomic methods.…
We study Fano schemes $F_k(X)$ for complete intersections $X$ in a projective toric variety $Y\subset \mathbb{P}^n$. Our strategy is to decompose $F_k(X)$ into closed subschemes based on the irreducible decomposition of $F_k(Y)$ as studied…
We prove the structure theorem of the intersection complexes of toric varieties in the category of mixed Hodge modules. This theorem is due to Bernstein, Khovanskii and MacPherson for the underlying complexes with rational coefficients. As…
We prove that the monodromy of an irreducible cohomologically complex rigid local system with finite determinant and quasi-unipotent local monodromies at infinity on a smooth quasiprojective complex variety $X$ is integral. This answers…
We introduce a new class of zero-dimensional weighted complete intersections, by abstracting the essential features of rational cohomology algebras of equal rank homogeneous spaces of compact connected Lie groups. We prove that, on a…