Related papers: The Synthetic Hilbert Additive Group Scheme

We describe an $E_k$-cell structure on the free $E_{k+1}$-algebra on a point, and more generally describe how the May-Milgram filtration of $\Omega^m \Sigma^m S^{k}$ lifts to a filtration of the free $E_{k+m}$-algebra on a point by iterated…

In the simplicial theory of hypercoverings, we replace the indexing category $\Delta$ by the \emph{symmetric simplicial category} $\Delta S$ and study (a class of) $\Delta S$-hypercoverings, which we call \emph{spaces admitting symmetric…

The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…

In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this…

The author and Nakano recently proved that multiplicities in a Specht filtration of a symmetric group module are well-defined precisely when the characteristic is at least five. This result suggested the possibility of a symmetric group…

We associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on classical (compactly supported) homology with Z/2 coefficients an analog…

In that paper, we recall the notion of the multidegree for $D$-modules, as exposed in a previous paper, with a slight simplification. A particular emphasis is given on hypergeometric systems, used to provide interesting and computable…

For an integer n>2 we define a polylogarithm, which is a holomorphic function on the universal abelian cover of C-{0,1} defined modulo (2 pi i)^n/(n-1)!. We use the formal properties of its functional relations to define groups lifting…

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping…

We define an $\infty$-category $\mathrm{CycSyn}$ of $p$-typical cyclotomic synthetic spectra and prove that the motivic filtration on $\mathrm{THH}(R;\mathbf{Z}_p)$, defined by Bhatt, Morrow, and Scholze when $R$ is quasisyntomic and by…

The theory of group lifting structures is applied to linear phase lifting factorizations for the two nontrivial classes of two-channel linear phase perfect reconstruction filter banks, the whole- and half-sample symmetric classes. Group…

Let G be a connected and reductive algebraic group over an algebraically closed field of characteristic p > 0. An interesting class of representations of G consists of those G-modules having a good filtration -- i.e. a filtration whose…

Let G be a semi simple linear algebraic group over a field of characteristic zero and let V be a finite dimensional irreducible G-module with highest weight vector v. Let P in G be the parabolic subgroup fixing v and let g=Lie(G). We get a…

We develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n=0$, as well as a certain duality for the $E_n$-(co)homology of…

Operadic tangent cohomology generalizes the existing cohomology theories of Chevalley--Eilenberg, Hochschild, and Harrison to address the deformation theory of general types of algebras through gadgets known as deformation complexes. The…

We investigate rational $G$-modules $M$ for a linear algebraic group $G$ over an algebraically closed field $k$ of characteristic $p > 0$ using filtrations by sub-coalgebras of the coordinate algebra $k[G]$ of $G$. Even in the special case…

Let $\H_n$ be a (degenerate or non-degenerate) Hecke algebra of type $G(\ell,1,n)$, defined over a commutative ring $R$ with one, and let $S(\bmu)$ be a Specht module for $\H_n$. This paper shows that the induced Specht module…

This work studies $t$-structures for the derived category of quasi-coherent sheaves on a quasi-compact quasi-separated algebraic stack. Specifically, using Thomason filtrations, we classify those $t$-structures which are generated by…

A classical approach to investigate a closed projective scheme $W$ consists of considering a general hyperplane section of $W$, which inherits many properties of $W$. The inverse problem that consists in finding a scheme $W$ starting from a…

Let $f: X \to S$ be a unipotent degeneration of projective complex manifolds over a disc such that the reduction of the central fibre $Y=f^{-1}(0)$ is simple normal crossings, and let $X_\infty$ be the canonical nearby fibre. Building on…