Related papers: An Artin-Rees Theorem and applications to zero cyc…
In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.
We show that for a large class of Artin groups with Dynkin diagrams being a tree, the $K(\pi,1)$-conjecture holds. We also establish the $K(\pi,1)$-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which…
This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example, and then give three examples which are relevant to current research. The focus…
In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.
For a smooth projective variety X over an arbitrary field k, we discuss the surjectivity of the Albanese map from the Chow group of zero-cycles of degree zero on X to the group of rational points of the Albanese variety of X. Over…
We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
In this paper, we give a new proof of an arithmetic analogue of the Riemann-Roch Theorem, due originally to Serge Lang. Lang's result was first proved using the lattice point geometry of Minkowski. By contrast, our proof is completely…
We give a simple and self-contained proof of an extension of a projection theorem of Bourgain over the reals to division algebras over local fields of zero characteristic.
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
We prove that the cycle-convergence of the restarted GMRES applied to a system of linear equations with a normal coefficient matrix is sublinear.
We give a complete description of all self-injective artin algebras of infinite representation type whose component quiver has no short cycles.
We give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact we show that this condition is also sufficient when the module is a…
We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory together with some basic commutative algebra of Artin rings.
The paper contains five examples of using cyclic bases of zero-curvature representations in studies of weak and strong Lax pairs, hierarchies of evolution systems, and recursion operators.
We introduce positive cones on algebras with involution. These allow us to prove analogues of Artin's solution to Hilbert's 17th problem, the Artin-Schreier theorem characterizing formally real fields, and to define signatures with respect…
The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic group to a ramified cover. A version of Bertini Theorem in this context is also obtained.
We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…
These notes are based on three lectures given by the first author as part of an introductory workshop at MSRI for the program in Commutative Algebra, 2012-13. The notes follow the talks, but there are extra comments and explanations, as…
We prove the generic base change theorem for stacks, and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables…
This is an essentially extended version of the preprint dated by August 2005 (this includes now the varieties of types F_4, E_6 and E_7). Let k be a field of characteristic not 2 and 3. Let G be an exceptional simple algebraic group of type…