Related papers: On the motivic Segal conjecture

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral…

We formulate and prove an analog of Poonen's finite-field Bertini theorem with Taylor conditions that holds in the Grothendieck ring of varieties. This gives a broad generalization of the work of Vakil-Wood, who treated the case of smooth…

In this note, we give a general method to obtain unstable motivic cell structures, following Wendt's application of the Bialynicki-Birula algebraic Morse theory. We then apply the method to spherical varieties, with special attention to the…

To an Adams-type homology theory we associate a notion of a synthetic spectrum, this is a product-preserving sheaf on the site of finite spectra with projective $E$-homology. We prove that the $\infty$-category $Syn_{E}$ of synthetic…

We prove two conjectures in this paper. The first conjecture is by Lund, Pham and Thu: Given a Borel set $A\subset \mathbb{R}^n$ such that $\dim A\in (k,k+1]$ for some $k\in\{1,\dots,n-1\}$. For $0<s<k$, we have \[ \text{dim}(\{y\in…

We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger-Murre and Corti-Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary…

Let $RG$ be the group ring of a finite group $G$ over a commutative ring $R$ with $1$. An element $x$ in $RG$ is said to be skew-symmetric with respect to an involution $\sigma$ of $RG$ if $\sigma(x)=-x.$ A structure theorem for the…

We show that Shipley's "detection functor" for symmetric spectra generalizes to motivic symmetric spectra. As an application, we construct motivic strict ring spectra representing morphic cohomology, semi-topological $K$-theory, and…

We show that the Conjecture of Voevodsky concerning slices of the algebraic cobordism spectrum MGL implies a general statement about the slices of motivic Landweber spectra. In particular it confirms the possible approach suggested by…

We verify a finiteness conjecture of Feit on sources of simple modules over group algebras for various classes of finite groups related to the symmetric groups.

In the paper M. Somekawa, {\it{On Milnor $K$-groups attached at semi-Abelian varieties}}, K-theory, \textbf{4} (1990) p.105, Somekawa conjectures that his Milnor K-group $K(k,G_1,...,G_r)$ attached to semi-abelian varieties $G_1$,...,$G_r$…

In this article we introduce and study a motivic category in the arithmetic of function fields, namely the category of motives over an algebraic closure $L$ of a finite field with coefficients in a global function field over this finite…

Given a Chevalley group $\mathcal{G}$ of classical type and a Borel subgroup $\mathcal{B} \subseteq \mathcal{G}$, we compute the $\Sigma$-invariants of the $S$-arithmetic groups $\mathcal{B}(\mathbb{Z}[1/N])$, where $N$ is a product of…

In this paper, we produce a cellular motivic spectrum of motivic modular forms over $\R$ and $\C$, answering positively to a conjecture of Dan Isaksen. This spectrum is constructed to have the appropriate cohomology, as a module over the…

Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This…

Symmetries and their applications always played an important role in I.E. Segal's work. I shall exemplify this, starting with his correct proof (at the Lie group level) of what physicists call the ``O'Raifeartaigh theorem", continuing with…

In a series of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc (CMPP) and then M. Primc put forth three remarkable sets of conjectures, stating that the generating functions of coloured integer partition in which the parts satisfy…

In this paper we prove a version of Deligne's conjecture for potentially automorphic motives, twisted by certain algebraic Hecke characters. The Hecke characters are chosen in such a way that we can use automorphic methods in the context of…

We prove the modulo $p$ and modulo $p^2$ cases of Igusa's conjecture on exponential sums. This conjecture predicts specific uniform bounds in the homogeneous polynomial case of exponential sums modulo $p^m$ when $p$ and $m$ vary. We…

Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot...\cdot(n_lg)$ where $g\in G$ and $n_1,\cdots,n_l\in[1,{\hbox{\rm ord}}(g)]$, and the index $\ind S$ of $S$ is defined to be the minimum…