An algebraic proof of Gabrielov's theorem about analytic homomorphisms in any characteristic

Homomorphisms of local algebras in positive characteristic

We investigate some properties of regularity of homomorphisms of local algebras over positive characteristic fields. We state a result of monomialization of such a homomorphism between algebras of analytic or algebraic power series. From this we deduce some extensions in positive characteristic of results due to S. Izumi and A. Gabrielov.

平坦仿射群概型的平坦性纤维判别法与同态

Fiber criteria for flatness and homomorphisms of flat affine group schemes

本文提出了避免“有限性”假设的模平坦性纤维判别法，并基于 Tannakian 观点推导了其在仿射与平坦群概型理论中的应用。

On rank Theorems for morphisms of local rings

We prove a generalization of Gabrielov's rank theorem for families of rings of power series which we call W-temperate. Examples include the families of complex analytic functions and of Eisenstein series. As a Corollary, we provide rank Theorems for convergent series in general characteristic zero complete valued fields (not necessarily algebraically closed, nor archimedean).

弱图同态理想的代数研究

An algebraic study of ideals of weak graph homomorphisms

引入弱图同态理想，刻画其幂具有线性分解的图对，并研究其无混合性、Cohen-Macaulay性、投射维数和正则度。

Algebraic properties of ideals of poset homomorphisms

Given finite posets $P$ and $Q$, we consider a specific ideal $L(P,Q)$, whose minimal monomial generators correspond to order-preserving maps $ϕ:P\rightarrow Q$. We study algebraic invariants of those ideals. In particular, sharp lower and upper bounds for the Castelnuovo-Mumford regularity and the projective dimension are provided. Precise formulas are obtained for a large subclass of these ideals. Moreover, we provide complete characterizations for several algebraic properties of $L(P,Q)$, including being Buchsbaum, Cohen-Macaulay, Gorenstein and having a linear resolution. We also give a pa…

Ideals of Graph Homomorphisms

In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by introducing the ideals of graph homomorphisms. For this new class of ideals we investigate how the topology of the graphs influence the algebraic properties. We describe explicit Grobner bases for several classes, generalizing results by Hibi, Sturmfels and Sullivant. One of our main tools is the toric fiber product, and we employ results by Engstrom, Kahle and S…