3 citations · 5 across the 11 of their papers we have counts for
12 papers · 1 filter
Topology of Galois conjugate character varieties
Junliang Shen, Siqing Zhang
We study the interaction between integral structures, automorphisms, and tautological relations for the cohomology of character varieties. Based on this, we propose a method to det…
Polynomiality of the Generalized Verschiebung Degree
Siqing Zhang
For a general curve in positive characteristic, taking the Frobenius pullback induces a generically finite rational map V on the moduli space of rank 2 vector bundles with trivial…
A note on Azumaya algebras and one-forms
Siqing Zhang
The crystalline differential operators on a smooth variety X give rise to a non-split Azumaya algebra over the cotangent bundle of the Frobenius twist X'. In some cases, this Azuma…
Logarithmic Non-Abelian Hodge Theory for curves in prime characteristic
Mark Andrea de Cataldo, Siqing Zhang
For a curve C and a reductive group G in prime characteristic, we relate the de Rham moduli of logarithmic G-connections on C to the Dolbeault moduli of logarithmic G-Higgs bundles…
Semistable Non Abelian Hodge theorem in positive characteristic
Andres Fernandez Herrero, Siqing Zhang
In this paper, we show that for any reductive group the moduli space of semistable -Higgs bundles on a curve in characteristic is a twisted form of the moduli space of s…
Meromorphic Hodge moduli spaces for reductive groups in arbitrary characteristic
Andres Fernandez Herrero, Siqing Zhang
Fix a smooth projective family of curves and a split reductive group scheme over a Noetherian base scheme . For any (possibly nonreduced) fixed relative Cartier di…
The de Rham stack and the variety of very good splittings of a curve
Mark Andrea A. de Cataldo, Michael Groechenig, Siqing Zhang
The stack of relative splittings of a special Azumaya algebra plays a key role in the Non-Abelian Hodge Theory for curves in positive characteristics. In this paper, we define and…
Geometry of the logarithmic Hodge moduli space (with an Appendix joint with Siqing Zhang)
Mark Andrea A. de Cataldo, Andres Fernandez Herrero
We show the smoothness over the affine line of the Hodge moduli space of logarithmic t-connections of coprime rank and degree on a smooth projective curve with geometrically integr…
Cohomology of the moduli of Higgs bundles via positive characteristic
Mark Andrea de Cataldo, Davesh Maulik, Junliang Shen +1
For any two degrees coprime to the rank, we construct a family of ring isomorphisms parameterized by GSp(2g) between the cohomology of the moduli spaces of stable Higgs bundles whi…
A Cohomological Non Abelian Hodge Theorem in Positive Characteristic
Mark Andrea A. de Cataldo, Siqing Zhang
We start with a curve over an algebraically closed ground field of positive characteristic . By using specialization techniques, under suitable natural coprimality conditions,…
Projective Completion of Moduli of -Connections on Curves in Positive and Mixed Characteristic
Mark Andrea A. de Cataldo, Siqing Zhang
We generalize a compactification technique due to C. Simpson in the context of -actions over the ground field of complex numbers, to the case of a universally Japanes…
Bott-Samelson-Demazure-Hansen Varieties for Projective Homogeneous Varieties with Nonreduced Stabilizers
Siqing Zhang
Over a field of positive characteristic, a semisimple algebraic group may have some nonreduced parabolic subgroup . In this paper, we study the Schubert and Bott-Samelson-De…