52 citations · 222 across the 40 of their papers we have counts for
51 papers
Splitting Brauer classes by genus one curves over number fields
Benjamin Antieau, Asher Auel, Federico Scavia
We prove that every Severi-Brauer variety of dimension at least two over a number field contains a twisted elliptic normal curve. Consequently, every Brauer class over a number fie…
The animation of the opposite of finite sets
Benjamin Antieau
We give a direct proof of the fact that the animation of the opposite of the category of finite sets is a 1-category.
Cyclotomic synthetic spectra
Benjamin Antieau, Noah Riggenbach
We define an -category of -typical cyclotomic synthetic spectra and prove that the motivic filtration on , defined by Bha…
Spectral sequences, décalage, and the Beilinson t-structure
Benjamin Antieau
This paper explains the theory of spectral sequences via décalage and the Beilinson t-structure.
On the -theory of
Benjamin Antieau, Achim Krause, Thomas Nikolaus
We give an explicit algebraic description, based on prismatic cohomology, of the algebraic K-groups of rings of the form where is a p-adic field and is a non-trivia…
Prismatic cohomology relative to -rings
Benjamin Antieau, Achim Krause, Thomas Nikolaus
We develop prismatic and syntomic cohomology relative to a -ring. This simultaneously generalizes Bhatt and Scholze's absolute and relative prismatic cohomology and shows that t…
Spherical Witt vectors and integral models for spaces
Benjamin Antieau
We give a new construction of the spherical Witt vector functor of Lurie and Burklund-Schlank-Yuan and extend it to nonconnective objects using synthetic spectra and recent work of…
Picard sheaves, local Brauer groups, and topological modular forms
Benjamin Antieau, Lennart Meier, Vesna Stojanoska
We prove that the Brauer group of TMF is isomorphic to the Brauer group of the derived moduli stack of elliptic curves. Then, we compute the local Brauer group, i.e., the subgroup…
On the K-theory of -- announcement
Benjamin Antieau, Achim Krause, Thomas Nikolaus
We announce new methods for using prismatic cohomology to compute the K-groups of and related rings. We use computer algebra methods to compute these K-groups thro…
The K-theory of perfectoid rings
Benjamin Antieau, Akhil Mathew, Matthew Morrow
We establish various properties of the p-adic algebraic K-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the p-adic K-theory…
Explicit descent on elliptic curves and splitting Brauer classes
Benjamin Antieau, Asher Auel
We prove new results on splitting Brauer classes by genus 1 curves, settling in particular the case of degree 7 classes over global fields. Though our method is cohomological in na…
The topological period-index conjecture
Benjamin Antieau, Ben Williams
We prove the topological analogue of the period-index conjecture in each dimension away from a small set of primes.
On the Beilinson fiber square
Benjamin Antieau, Akhil Mathew, Matthew Morrow +1
Using topological cyclic homology, we give a refinement of Beilinson's -adic Goodwillie isomorphism between relative continuous -theory and cyclic homology. As a result, we g…
Valuation rings are derived splinters
Benjamin Antieau, Rankeya Datta
We give three proofs that valuation rings are derived splinters: a geometric proof using the absolute integral closure, a homological proof which reduces the problem to checking th…
Descent for semiorthogonal decompositions
Benjamin Antieau, Elden Elmanto
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived ca…
Counterexamples to Hochschild--Kostant--Rosenberg in characteristic
Benjamin Antieau, Bhargav Bhatt, Akhil Mathew
We give counterexamples to the degeneration of the HKR spectral sequence in characteristic , both in the untwisted and twisted settings. We also prove that the de Rham--$\mathrm…
Derived invariants from topological Hochschild homology
Benjamin Antieau, Daniel Bragg
We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their…
Rational points and derived equivalence
Nicolas Addington, Benjamin Antieau, Sarah Frei +1
We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and the other does not. We begin with torsors ove…
On the uniqueness of infinity-categorical enhancements of triangulated categories
Benjamin Antieau
We study the problem of when triangulated categories admit unique infinity-categorical enhancements. Our results use Lurie's theory of prestable infinity-categories to give concept…
Cartier modules and cyclotomic spectra
Benjamin Antieau, Thomas Nikolaus
We construct and study a t-structure on p-typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this t-structure.…
Periodic cyclic homology and derived de Rham cohomology
Benjamin Antieau
We use the Beilinson -structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies…
A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p
Benjamin Antieau, Gabriele Vezzosi
We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smooth proper schemes in characteristic when . The best known previous result of this kind,…
On the Blumberg-Mandell Künneth theorem for TP
Benjamin Antieau, Akhil Mathew, Thomas Nikolaus
We give a new proof of the recent Künneth theorem for periodic topological cyclic homology (TP) of smooth and proper dg categories over perfect fields of characteristic p>0 due to…
Some remarks on topological -theory of dg categories
Benjamin Antieau, Jeremiah Heller
Using techniques from motivic homotopy theory, we prove a conjecture of Anthony Blanc about semi-topological K-theory of dg categories with finite coefficients. Along the way, we s…