3 citations · 9 across the 10 of their papers we have counts for
9 papers · 1 filter
The higher direct images of locally constant group schemes from the Kummer log flat topology to the classical flat topology
Heer Zhao
Let be an fs log scheme, and let be a group scheme over the underlying scheme which is étale locally representable by (1) a finite dimensional -vector space, or…
Comparison of Kummer logarithmic topologies with classical topologies II
Heer Zhao
We show that the higher direct images of smooth commutative group schemes from the Kummer log flat site to the classical flat site are torsion. For (1) smooth affine commutative sc…
Log p-divisible groups associated to log 1-motives
Matti Würthen, Heer Zhao
We first provide a detailed proof of Kato's classification theorem of log -divisible groups over a noetherian henselian local ring. Exploring Kato's idea further, we then define…
Extending finite subgroup schemes of semi-stable abelian varieties via log abelian varieties
Heer Zhao
For a semi-stable abelian variety A_K over a complete discrete valuation field K, we show that every finite subgroup scheme of A_K extends to a log finite flat group scheme over th…
Extending tamely ramified strict 1-motives into ket log 1-motives
Heer Zhao
We define ket abelian schemes, ket 1-motives, and ket log 1-motives, and formulate duality theory for these objects. Then we show that tamely ramified strict 1-motives over a compl…
Comparison of Kummer logarithmic topologies with classical topologies
Heer Zhao
We compare the Kummer flat (resp. Kummer etale) cohomology with the flat (resp. etale) cohomology with coefficients in smooth commutative group schemes, finite flat group schemes a…
Log abelian varieties over a log point
Heer Zhao
We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian var…
Degenerating abelian varieties via log abelian varieties
Heer Zhao
For any split totally degenerate abelian variety over a complete discrete valuation field, we construct a log abelian variety over the discrete valuation ring extending the given a…
Tame stacks and log flat torsors
Jean Gillibert, Heer Zhao
We compare tame actions in the category of schemes with torsors in the category of log schemes endowed with the log flat topology. We prove that actions underlying log flat torsors…