51 citations · 235 across the 34 of their papers we have counts for
39 papers
Keller sequences of exact -categories
Yonatan Harpaz, Daniel Marlowe
We study a family of fibre-cofibre sequences in the -category of exact -categories, which we call Keller sequences, generalising the notion of Verdier sequences of…
Deformation theory and cotangent complex of dg operads
Yonatan Harpaz, Truong Hoang
In the first part, we give an explicit description of the cotangent complex of differential graded (dg) operads, modeled as an operadic infinitesimal bimodule. This leads to a unif…
Trace methods for stable categories I: The linear approximation of algebraic K-theory
Yonatan Harpaz, Thomas Nikolaus, Victor Saunier
We study algebraic K-theory and topological Hochschild homology in the setting of bimodules over a stable category, a datum we refer to as a laced category. We show that in this se…
A motivic spectrum representing hermitian K-theory
Baptiste Calmès, Yonatan Harpaz, Denis Nardin
We establish fundamental motivic results about hermitian K-theory without assuming that 2 is invertible on the base scheme. In particular, we prove that both quadratic and symmetri…
Supersolvable descent for rational points
Yonatan Harpaz, Olivier Wittenberg
We construct an analogue of the classical descent theory of Colliot-Thélène and Sansuc in which algebraic tori are replaced with finite supersolvable groups. As an application, we…
Rational points on fibrations with few non-split fibres
Yonatan Harpaz, Dasheng Wei, Olivier Wittenberg
We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its depend…
Cartesian Fibrations of -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
In this article we introduce four variance flavours of cartesian 2-fibrations of -bicategories with -bicategorical fibres, in the framework of scaled simplicial set…
Bilimits are Bifinal Objects
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
We prove that a (lax) bilimit of a 2-functor is characterized by the existence of a limiting contraction in the 2-category of (lax) cones over the diagram. We also investigate the…
Stable moduli spaces of hermitian forms
Fabian Hebestreit, Wolfgang Steimle
We prove that Grothendieck-Witt spaces of Poincaré categories are, in many cases, group completions of certain moduli spaces of hermitian forms. This, in particular, identifies Kar…
Fibrations and lax limits of -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
We study four types of (co)cartesian fibrations of -bicategories over a given base , and prove that they encode the four variance flavors of -inde…
On k-invariants for -categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
Every -category can be approximated by its tower of homotopy -categories. In this paper, we prove that the successive stages of this tower are classified by k-…
Hermitian K-theory for stable -categories III: Grothendieck-Witt groups of rings
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We establish a fibre sequence relating the classical Grothendieck-Witt theory of a ring to the homotopy -orbits of its K-theory and Ranicki's original (non-period…
Hermitian K-theory for stable -categories II: Cobordism categories and additivity
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We define Grothendieck-Witt spectra in the setting of Poincaré -categories and show that they fit into an extension with a K- and an L-theoretic part. As consequences we de…
Hermitian K-theory for stable -categories I: Foundations
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
This paper is the first in a series in which we offer a new framework for hermitian K-theory in the realm of stable -categories. Our perspective yields solutions to a varie…
Gray tensor products and lax functors of -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
We give a definition of the Gray tensor product in the setting of scaled simplicial sets which is associative and forms a left Quillen bifunctor with respect to the bicategorical m…
On the equivalence of all models for -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
The goal of this paper is to provide the last equivalence needed in order to identify all known models for -categories. We do this by showing that Verity's model of sat…
The Massey vanishing conjecture for number fields
Yonatan Harpaz, Olivier Wittenberg
A conjecture of Mináč and Tân predicts that for any n>2, any prime p and any field k, the Massey product of n Galois cohomology classes in H^1(k,Z/pZ) must vanish if it is defined.…
Lax limits of model categories
Yonatan Harpaz
For a diagram of simplicial combinatorial model categories, we show that the associated lax limit, endowed with the projective model structure, is a presentation of the lax limit o…
Number fields with prescribed norms
Christopher Frei, Daniel Loughran, Rachel Newton +2
We study the distribution of extensions of a number field with fixed abelian Galois group , from which a given finite set of elements of are norms. In particular, we sho…
Quillen cohomology of -categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
In this paper we study the homotopy theory of parameterized spectrum objects in the -category of -categories, as well as the Quillen cohomology of an $(\infty,…
The tangent bundle of a model category
Yonatan Harpaz, Joost Nuiten, Matan Prasma
This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category satisfy…
Second descent and rational points on Kummer varieties
Yonatan Harpaz
A powerful method pioneered by Swinnerton-Dyer allows one to study rational points on pencils of curves of genus 1 by combining the fibration method with a sophisticated form of de…
Ambidexterity and the universality of finite spans
Yonatan Harpaz
Pursuing the notions of ambidexterity and higher semiadditivity as developed by Hopkins and Lurie, we prove that the span -category of -finite spaces is the free -sem…
The abstract cotangent complex and Quillen cohomology of enriched categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
In his fundamental work, Quillen developed the theory of the cotangent complex as a universal abelian derived invariant, and used it to define and study a canonical form of cohomol…