Related papers: $p$-adic vanishing cycles as Frobenius-fixed point…

The primary goal of this paper is to systematically exploit the method of Deligne-Illusie to obtain Kodaira type vanishing theorems for vector bundles and more generally coherent sheaves on algebraic varieties. The key idea is to introduce…

In the 1960s, Dwork developed a p-adic cohomology theory of de Rham type for varieties over finite fields, based on a trace formula for the action of a Frobenius operator on certain spaces of p-adic analytic functions. One can consider a…

Given a finite set of closed rational points of affine space over a field, we give a Gr\"obner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the…

Using the de Rham stack of Bhatt-Lurie and Drinfeld, we prove that de Rham complex of a smooth quasi-F-split variety over a perfect field of positive characteristic decomposes in all degrees. In particular, smooth proper quasi-F-split…

This is the first part of the project toward proving the BCOV's Feymann graph sum formula of all genera Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, we introduce the notion of N-Mixed-Spin-P fields, construct…

We propose a simple method for the computation of the flat coordinates and Saito primitive forms on Frobenius manifolds of the deformations of Jacobi rings associated with isolated singularities. The method is based on using a conjecture…

In this paper we study $p$-adic dynamical systems generated by the function $f(x)={a\over x^2}$ in the set of complex $p$-adic numbers. We find an explicit formula for the $n$-fold composition of $f$ for any $n\geq 1$. Using this formula we…

We use the $p$-divisible group attached to a 1-motive to generalize the conjugate $p$-adic uniformization of Iovita--Morrow--Zaharescu to arbitrary $p$-adic formal semi-abelian schemes or $p$-divisible groups over the ring of integers in a…

We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field $\mathbb{F}_q$ whose characteristic polynomial (of Frobenius) is square-free and of abelian varieties defined over the prime field…

This is a survey of the known properties of Iwasawa algebras, which are completed group rings of compact p-adic analytic groups with coefficients the ring Zp of p-adic integers or the field Fp of p elements. A number of open questions are…

In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast…

In the framework of adelic approach we consider real and p-adic properties of dynamical system given by linear fractional map f (x) = (a x + b)/(c x + d), where a, b, c and d are rational numbers. In particular, we investigate behavior of…

In ``New Proofs of the structure theorems for Witt Rings'', Lewis shows how the standard ring-theoretic results on the Witt ring can be deduced in a quick and elementary way from the fact that the Witt ring of a field is integral and from…

We generalize the results of Chang-Li, Kim-Oh and Chang-Li on the moduli of $p$-fields to the setting of (quasi-)maps to complete intersections in arbitrary smooth Deligne-Mumford stacks with projective coarse moduli. In particular, we show…

The homological conjectures, which date back to Peskine, Szpiro and Hochster in the late sixties, make fundamental predictions about syzygies and intersection problems in commutative algebra. They were settled long ago in the presence of a…

Let $M$ be a multiplicative monoid with identity. Then I show that there is a universal one dimensional formal group law equipped with an action of $M$. If $M$ is $p$-perfect (i.e. $m\mapsto m^p$ is an isomorphism for some prime number $p$)…

In this paper, we associate to every $p$-adic representation $V$ a $p$-adic differential equation $\mathbf{D}^{\dagger}_{\mathrm{rig}}(V)$, that is to say a module with a connection over the Robba ring. We do this via the theory of…

We give a characterization of finitely ramified $\omega$-pseudo complete valued fields of mixed characteristic $(0, p)$, with fixed residue field $k$ and value group $G$ of cardinality $\aleph_{1}$, in terms of a Hahn-like construction over…

We consider chaining multiplicative-inverse operations in finite fields under alternating polynomial bases. When using two distinct polynomial bases to alternate the inverse operation we obtain a partition of $\mathbb F_{p^n}\setminus…

This is an exposition of work on Artin's Conjecture on the zeros of $p$-adic forms. A variety of lines of attack are described, going back to 1945. However there is particular emphasis on recent developments concerning quartic forms on the…