Related papers: Mod $p$ Buchstaber invariant

Buchstaber invariant is a numerical characteristic of a simplicial complex, arising from torus actions on moment-angle complexes. In the paper we study the relation between Buchstaber invariants and classical invariants of simplicial…

Let p be a prime number. The Hasse invariant is a modular form modulo p that is often used to produce congruences between modular forms of different weights. We show how to produce such congruences between forms of weights 2 and p+1, in…

In this article, we prove that Buchstaber invariant of 4-dimensional real universal complex is no less than 24 as a follow-up to the work of Ayzenberg and Sun. Moreover, a lower bound for Buchstaber invariants of $n$-dimensional real…

In this paper we study the Buchstaber invariant of simplicial complexes, which comes from toric topology. With each simplicial complex $K$ on $m$ vertices we can associate a moment-angle complex $\mathcal Z_K$ with a canonical action of the…

We will prove several congruences modulo a power of a prime such as $$ \sum_{0<k_1<...<k_{n}<p}\leg{p-k_{n}}{3} {(-1)^{k_{n}}\over k_1... k_{n}}\equiv {lll} -{2^{n+1}+2\over 6^{n+1}} p B_{p-n-1}({1\over 3}) &\pmod{p^2} &{if $n$ is odd}…

We show that an elliptic modular form with integral Fourier coefficients in a number field $K$, for which all but finitely many coefficients are divisible by a prime ideal $\frak{p}$ of $K$, is a constant modulo $\frak{p}$. A similar…

In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit…

The $c_2$ invariant is an arithmetic graph invariant related to quantum field theory. We give a relation modulo $p$ between the $c_2$ invariant at $p$ and the $c_2$ invariant at $p^s$ by proving a relation modulo $p$ between certain…

We study stable vector bundles over the modular curve X(p) corresponding to the principal congruence subgroup of the modular group of prime level p which are invariant with respect to its automorphism group.

Let $F$ be any field of characteristic $p$. It is well-known that there are exactly $p$ inequivalent indecomposable representations $V_1,V_2,...,V_p$ of $C_p$ defined over $F$. Thus if $V$ is any finite dimensional $C_p$-representation…

Let $p$ be an odd prime and let $d\in\{2,3,7\}$. When $(\frac{-d}p)=1$ we can write $p=x^2+dy^2$ with $x,y\in\mathbb Z$; in this paper we aim at determining $x$ or $y$ modulo $p^2$. For example, when $p=x^2+3y^2$, we show that if $p\equiv…

We investigate equivariant and invariant topological complexity of spheres endowed with smooth non-free actions of cyclic groups of prime order. We prove that semilinear $\mathbb{Z}/p$-spheres have both invariants either $2$ or $3$ and…

For primes $p$, we investigate an $\mathbb{F}_p$-version of simplicial volume and compare these invariants with their siblings over other coefficient rings. We will also consider the associated gradient invariants, obtained by stabilisation…

The author proves variants of Buchstab's identity on sieve functions, refining the previous work on new iteration rules of Brady. The main tool used in the proof is a special form of combinatorial identities related to the binomial…

We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in characteristic zero. We discuss the connection between the…

A topological invariant of a polynomial map $p:X\to B$ from a complex surface containing a curve $C\subset X$ to a one-dimensional base is given by a rational second homology class in the compactification of the moduli space of genus $g$…

In this paper we study a new combinatorial invariant of simple polytopes, which comes from toric topology. With each simple n-polytope P with m facets we can associate a moment-angle complex Z_P with a canonical action of the torus T^m.…

We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain finite p-groups. The case of base fields of characteristic p…

The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can for each odd prime $p$, determine…

Given a prime $p\geq 5$, we reduce modulo p a convolution of order p-1 of powers of two weighted Bernoulli numbers with Bernoulli numbers in terms of harmonic numbers and generalized harmonic numbers. Our proof is based on studying the…