Related papers: The algebraic Novikov spectral sequence for topolo…

We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of…

Let kq denote the very effective cover of the motivic Hermitian K-theory spectrum. We analyze the ring of cooperations $\pi^\mathbb{R}_{**}(\text{kq} \otimes \text{kq})$ in the stable motivic homotopy category $\text{SH}(\mathbb{R})$,…

We construct an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G and show it is of finite injective dimension. It can be used as a model for rational $G$-spectra in the sense that there is a homology…

We define a new cyclic module, dual to the Connes-Moscovici cyclic module, for Hopf algebras, and give a characteristric map for the coaction of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras,…

We study a particular family of elements in the cohomology of the $\mathbb{C}$-motivic Steenrod algebra, also known as the $\mathbb{C}$-motivic Adams $E_2$-page. This family exhibits unusual periodicity properties, and it is related both to…

In this article, we extend the computation of topological Hochschild homology (THH) of the Adams summand $\ell$ of $p$-local connective complex topological K-theory ($ku$) to $ku$ itself. We leverage the relation $u^{p-1} = v_1$, where $u$…

This document contains large-format Adams charts that compute 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. The charts are essentially complete through the 61-stem and contain partial…

We use the Adams spectral sequence to compute the KO-theory of all toric manifolds and certain singular toric varieties.

We compute the $E_2$ pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three spatial dimensions, considering the cell decomposition in…

Let $K$ be a perfect field and let $E$ be a homotopy commutative ring spectrum in the Morel-Voevodsky stable motivic homotopy category $\mathcal{SH}(K)$. In this work we investigate the relation between the $E$-homology localization and…

For an arbitrary compact Lie group G, we describe a model for rational G-spectra with toral geometric isotropy and show that there is a convergent Adams spectral sequence based on it. The contribution from geometric isotropy at a subgroup K…

We study the mod-2 cohomology spectral sequence arising from delooping the Bousfield-Kan cosimplicial space giving the 2-nilpotent completion of a connective spectrum $X$. Under good conditions its $E_{2}$-term is computable as certain…

Elliptic modular graph forms (eMGFs) are non-holomorphic modular forms depending on a modular parameter $\tau$ of a torus and marked points $z$ thereon. Traditionally, eMGFs are constructed from nested lattice sums over the discrete momenta…

We compute the homotopy groups of the $C_2$ fixed points of equivariant topological modular forms at the prime $2$ using the descent spectral sequence. We then show that as a $\mathrm{TMF}$-module, it is isomorphic to the tensor product of…

We compute modular forms known to arise from the order 5 generators of the 5-local Adams-Novikov spectral sequence 2-line, generalizing and contextualizing previous computations of M. Behrens and G. Laures. We exhibit analogous computations…

Let $\Phi\to \Gamma\to \Sigma$ be a conormal extension of Hopf algebras over a commutative ring $k$, and let $M$ be a $\Gamma$-comodule. The Cartan-Eilenberg spectral sequence $$ E_2 = \mathrm{Ext}_\Phi(k,\mathrm{Ext}_\Sigma(k,M)) \implies…

For every normalized newform f in S_2(Gamma_1(N)) with complex multiplication, we study the modular parametrizations of elliptic curves C from the abelian variety A_f. We apply the results obtained when C is Gross's elliptic curve A(p).

We compute the motivic Milnor fiber of a complex plane curve singularity in an inductive and combinatoric way using the extended simplified resolution graph. The method introduced in this article has a consequence that one can study the…

We construct a multiplicative spectral sequence converging to the cohomology algebra of the diagonal complex of a bisimplicial set with coefficients in a field. The construction provides a spectral sequence converging to the cohomology…

We consider the moduli space of holomorphic principal bundles for reductive Lie groups over Riemann surfaces (possibly with boundaries) and equipped with meromorphic connections. We associate to this space a point-wise notion of quantum…