We construct a p-adic version of Elliptic Cohomology whose coefficient ring agrees with Serre’s ring of p-adic modular forms. We then construct a stable operation Ûp in this theory agreeing with Atkin’s operator Up on p-adic modular forms. Throughout the paper we assume given a fixed prime p ≥ 5. We begin as in [2] by considering the universal Weierstrass cubic (for Z(p) algebras) Ell/R∗: Ell:Y...

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

An equigenerated monomial ideal $$I$$ in the polynomial ring $$R=k[z_1,\ldots, z_n]$$ is a Freiman if $$\mu(I^2)=\ell(I)\mu(I)-{\ell(I)\choose 2}$$ , where $$\ell(I)$$ analytic spread of and $$\mu(I)$$ number minimal generators . In this paper we classify all simple connected unmixed bipartite graphs whose cover ideals are ideals.

Richardson varieties are obtained as intersections of Schubert and opposite varieties. We provide a new family toric degenerations inside Grassmannians by studying Gröbner their corresponding ideals. These parametrised block diagonal matching fields in the sense Sturmfels [33]. associate weight vector to each field study its initial ideal. In particular, we characterise when such ideals toric, ...

For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...

This work explores some connections between the elliptic cohomology of classifying spaces for finite groups, Virasoro equivariant bundles over their loop spaces and Moonshine for finite groups. Our motivation is as follows: up to homotopy we can replace the loop group LBG by the disjoint union ⨿ [γ]BCG(γ) of classifying spaces of centralizers of elements γ representing conjugacy classes of elem...

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

We compare the cohomology ring of flag variety ${\\mathcal{F}\\ell}n$ and Chow Gelfand–Zetlin toric $X{\\operatorname{GZ}}$.We show that $H^(\\mathcal{F}{\\ell}\_n, \\mathbb{Q})$ is Poincaré duality quotient subalgebra $A^(X\_{\\operatorname{GZ}}, generated by degree $1$ elements. compute these algebras for $n=3$ see that, in general, this does not have duality.

Let K be a field and let $$S=K[x_1,\ldots ,x_n]$$ standard polynomial ring over K. We characterize the extremal Betti numbers, values as well positions, of t-spread strongly stable ideal S. Our approach is constructive. Indeed, given some positive integers $$a_1,\dots ,a_r$$ pairs $$(k_1,\ell _1),\ldots ,(k_r,\ell _r)$$ , we are able to determine under which conditions there exists I S with $$\...