40 citations · 150 across the 28 of their papers we have counts for
29 papers
Singular varieties and infinitesimal non-commutative Witt vectors
Phùng Hô Hai, João Pedro dos Santos, Đào Văn Thinh
Given a projective variety over an algebraically closed field , M. V. Nori introduced in 1976 a group scheme which accounts for principal bundles with finite…
Fiber criteria for flatness and homomorphisms of flat affine group schemes
Phùng Hô Hai, Hop D. Nguyen, João Pedro dos Santos
A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finit…
Prolongation of regular singular connections on punctured affine line over a Henselian ring
Phùng Hô Hai, João Pedro dos Santos, Pham Thanh Tâm +1
We generalize Deligne's equivalence between the categories of regular-singular connections on the formal punctured disk and on the punctured affine line to the case where the base…
Algebraic theory of formal regular-singular connections with parameters
Phùng Hô Hai, João Pedro dos Santos, Pham Thanh Tâm
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over and $\mathbb…
Connections on trivial vector bundles over projective schemes
Indranil Biswas, Phùng Hô Hai, João Pedro dos Santos
Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In…
Regular-singular connections on relative complex schemes
Phùng Hô Hai, João Pedro dos Santos
Deligne's celebrated "Riemann--Hilbert correspondence" relates representations of the fundamental group of a smooth complex algebraic variety and regular-singular integrable connec…
Finite torsors on projective schemes defined over a discrete valuation ring
Phung Ho Hai, Joao Pedro dos Santos
Given a Henselian and Japanese discrete valuation ring and a flat and projective -scheme , we follow the approach of Biswas-dos Santos to introduce a full subcategory of…
On the fundamental group schemes of certain quotient varieties
Indranil Biswas, Phùng Hô Hai, João Pedro dos Santos
In \cite{armstrong}, M. Armstrong proved a beautiful result describing fundamental groups of quotient spaces. In this paper we prove an analogue of Armstrong's theorem in the setti…
Jacobi-Trudi type formula for character of irreducible representations of
Nguyen Luong Thai Binh, Nguyen Thi Phuong Dung, Phung Ho Hai
We prove a determinantal type formula to compute the irreducible characters of the general Lie superalgebra in terms of the characters of the symmetric powers…
On the structure of affine flat group schemes over discrete valuation rings, II
Phùng Hô Hai, João Pedro dos Santos
In the 1st part of this work [DHdS18], we studied affine group schemes over a discrete valuation ring (DVR) by means of Neron blowups. We also showed how to apply these findings to…
The action of the étale fundamental group scheme on the connected component of the essentially finite one
Phùng Hô Hai, João Pedro P. dos Santos
We follow the pattern in a recent paper of Otabe [Ota15] to define an action of the étale fundamental group scheme on the local component of the essentially finite…
On the structure of affine flat group schemes over discrete valuation rings
Nguyen Dai Duong, Phung Ho Hai, João Pedro P. dos Santos
We study affine group schemes over a discrete valuation ring using two techniques: Neron blowups and Tannakian categories. We employ the theory developed to define and study di…
On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over discrete valuation rings
Nguyen Dai Duong, Phung Ho Hai, Nguyen Huy Hung
We study the flatness and the projectivity of Hopf algebras, defined over a Dedekind ring, over their Hopf subalgebras. We give a criterion for the faithful flatness and use it to…
On an injectivity lemma in the proof of Tannakian duality
Phùng Hô Hai
In this short work we give a very short and elementary proof of the injectivity lemma, which plays an important role in the Tannakian duality for Hopf algebras over a field. Based…
Tannakian duality over Dedekind rings and applications
Nguyen Dai Duong, Phùng Hô Hai
We establish a duality between flat affine group schemes and rigid tensor categories equipped with a neutral fiber functor (called Tannakian lattice), both defined over a Dedekind…
Gauss-Manin stratification and stratified fundamental group schemes
Phùng Hô Hai
We defined the Gauß-Manin stratification of a stratified bundle with respect to a smooth morphism and use it to study the homotopy sequence of stratified fundamental group schemes.
On the homotopy exact sequence for Nori's fundamental group
Hélène Esnault, Phùng Hô Hai, Eckart Viehweg
Unlike Grothendieck's étale fundamental group, Nori's fundamental group does not fulfill the homotopy exact sequence in general. We give necessary and sufficient conditions which f…
Packets in Grothendieck's Section Conjecture
Hélène Esnault, Phùng Hô Hai
Using the identification of sections of the Galois group of the ground field into the arithmetic fundamental group with neutral fiber functors of the category of finite connections…
On Nori's Fundamental Group Scheme
Hélène Esnault, Phùng Hô Hai, Xiaotao Sun
We determine the quotient category which is the representation category of the kernel of the homomorphism from Nori's fundamental group scheme to its étale and local parts. Pierre…
On the representation categories of matrix quantum groups of type
Phung Ho Hai
A quantum groups of type is defined in terms of a Hecke symmetry. We show in this paper that the representation category of such a quantum group is uniquely determined as an ab…
The Uniqueness Of Integrals On Hopf Algebras, A categorical approach
Phung Ho Hai, Nguyen Huy Hung
We propose a new method to investigate the dimension of the space of integrals on a Hopf algebra and other properties of -comodules.
On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries
Nguyen Phuong Dung, Phung Ho Hai
Hecke symmetries generalize the usual tensor symmetry of vector spaces $v\otimes w\arrow w\otimes v$ as well as the symmetry of vector superspaces. To a Hecke symmetry there as…
The homological determinant of quatum groups of type A
Phung Ho Hai
A quantum group of type A is defined as a Hopf algebra associated to a Hecke symmetry. We show the homology of a Koszul complex associated to the Hecke symmetry is one dimensional…
Tannaka-Krein duality for Hopf algebroids
Phung Ho Hai
We develop the Tannaka-Krein duality for monoidal functors with target in the categories of bimodules over a ring. The $\coend$ of such a functor turns out to be a Hopf algebroid o…