Related papers: A Simple Application of Enriques-Severi-Zariski-Se…
We prove that the Local Fundamental Group Scheme satisfies the Lefschetz - Bott theorems in characteristic p. The proofs are standard applications of the Enriques-Severi -Zariski-Serre vanishing theorems and known facts about the…
We define the local fundamental group scheme, defined by the F-trivial vector bundles, and give necessary and sufficient conditions for it to base change.
In this paper, the notion of local algebraic fundamental groups of normal complex analytic singularities are generalized to certain profinite groups called $D$-local algebraic fundamental groups which turns out to be useful even for the…
We prove a strengthening of the Grothendieck-Lefschetz hyperplane theorem for local Picard groups conjectured by Koll\'ar. Our approach, which relies on acyclicity results for absolute integral closures, also leads to a restriction theorem…
We propose a strengthening of the Grothendieck--Lefschetz hyperplane theorem for the local Picard group, prove some special cases and derive several consequences to the deformation theory of log canonical singularities. Version 2: Main…
We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.
We prove a Grothendieck-Lefschetz theorem for equivariant Picard groups of non-singular varieties with finite group actions.
We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixed base locus. We give several applications, including (1)…
We study Lefschetz fixed point formulas for constructible sheaves with higher-dimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions…
We prove a local-global principle for torsors under the prosolvable geometric fundamental group of a hyperbolic curve over a number field.
We prove a local-global principle for torsors under the prosolvable geometric fundamental group of an affine curve over a number field.
I propose an analogue in the first Heisenberg group $\mathbb{H}$ of David and Semmes' local symmetry condition (LSC). For closed $3$-regular sets $E \subset \mathbb{H}$, I show that the (LSC) is implied by the $L^{2}(\mathcal{H}^{3}|_{E})$…
The purpose of this paper is to give a proof of the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level in the even dimensional fiber case. The proof is, roughly speaking, an…
Let $k$ be a field, $X$ a connected scheme proper over $k$, $D\subsetneq X$ an ample effective connected divisor, $x\in D(k)$. For Tannakian categories $\mathcal{C}_X$ and $\mathcal{C}_D$ whose objects consist of vector bundles on $X$ and…
A general Lefschetz formula for the geodesic action on locally symmetric spaces is proven.
We compute the class groups of very general normal surfaces in complex projective three-space containing an arbitrary base locus $Z$, thereby extending the classic Noether-Lefschetz theorem (the case when $Z$ is empty). Our method is an…
We consider local-global principles for torsors under linear algebraic groups, over function fields of curves over complete discretely valued fields. The obstruction to such a principle is a version of the Tate-Shafarevich group; and for…
An old result by Shearer relates the Lov\'asz Local Lemma with the independent set polynomial on graphs, and consequently, as observed by Scott and Sokal, with the partition function of the hard core lattice gas on graphs. We use this…
We present a simple-to-apply criterion for recognizing topological groups that are (locally) homeomorphic to LF-spaces.
In this paper, we prove a Lefschetz-Riemann-Roch theorem for singular projective schemes which admit diagonalisable group scheme actions, this result generalizes P. Baum, W. Fulton and G. Quart's Lefschetz-Riemann-Roch theorem for singular…