Related papers: The Deligne-Illusie Theorem and exceptional Enriqu…

We define the Witt coindex of a link with non-trivial Alexander polynomial, as a concordance invariant from the Seifert form. We show that it provides an upper bound for the (locally flat) slice Euler characteristic of the link, extending…

We show that in a smooth family of complete varieties, the existence of full exceptional collection on a fiber preserves for the fibers in a neighborhood. Then we show that the noncommutative deformations of a strong exceptional collection…

We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary…

A linear mapping upon real n-dimensional space, where the dimension n is odd, has a real eigenvalue-eigenvector pair. The corresponding statement for complex vector spaces holds true for any dimension n, but should be easy to demonstrate…

We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of…

We show that $\kgl$-linear cohomology theories over an affine Dedekind scheme $S$ admit a canonical weight filtration on resolvable motives without inverting residual characteristics. Combined with upcoming work of Annala--Hoyois--Iwasa,…

We give a complete classification of Q_l-cohomology projective planes with isolated ADE-singularities and numerically trivial canonical bundle in odd characteristic. This leads to a beautiful relation with certain Enriques surfaces which…

We extend Lax-Phillips' theorem on discreteness of pseudo-cuspforms, in the style of Colin de Verdi{\`e}re's use of the Friedrichs self-adjoint extension of a restriction of the Laplace-Beltrami operator, as opposed to the use of semigroup…

We answer negatively an open problem of Illusie on the DR-decomposability of the log de Rham complex of the special fiber of a semi-stable reduction over the Witt ring. We also show that $E_1$ degeneration of the Hodge to log de Rham…

We generalize Illusie's result to prove the decomposition of the de Rham complex with smooth horizontal coefficients for a semistable $S$-morphism $f:X\ra Y$ which is liftable over $\Z/p^2\Z$. As an application, we prove the Koll\'ar…

We prove a Hochschild--Konstant--Rosenberg (HKR) theorem for arbitrary derived Deligne--Mumford (DM) stacks, extending the results of Arinkin-C\u{a}ld\u{a}raru-Hablicsek in the smooth, global quotient case, although with different methods.…

We give a concrete description of the category of etale algebras over the ring of Witt vectors of a given finite length with entries in an arbitrary ring. We do this not only for the classical p-typical and big Witt vector functors but also…

To every morphism $\chi\colon L\to M$ of differential graded Lie algebras we associate a functors of artin rings $\Def_\chi$ whose tangent and obstruction spaces are respectively the first and second cohomology group of the cylinder of…

We generalise Simpson's nonabelian Hodge correspondence to the context of projective varieties with klt singularities. The proof relies on a descent theorem for numerically flat vector bundles along birational morphisms. In its simplest…

Using techniques of A^1-homotopy theory, we produce motivic lifts of elements in classical homotopy groups of spheres; these lifts provide polynomial maps of spheres and allow us to construct ``low rank'' algebraic vector bundles on…

I consider the class of surfaces $X$ over algebraically closed fields with numerical invariants given in the title. In characteristic zero, this class contains fake projective planes which were introduced by David Mumford. I prove that in…

In these notes we give a brief introduction to decomposition theory and we summarize some classical and well-known results. The main question is that if a partitioning of a topological space (in other words a decomposition) is given, then…

We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely,…

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…

Given a unital ring $R$ and a two-sided ideal $I$ of $R$, we consider the question of determining when a unit of $R/I$ can be lifted to a unit of $R$. For the wide class of separative exchange ideals $I$, we show that the only obstruction…