research

I study Brauer groups, derived algebraic geometry, and algebraic K-theory.

publications and preprints

[46] B. Antieau, A. Krause, and T. Nikolaus, Prismatic cohomology relative to $\delta$-rings, [arxiv:2310].

[45] B. Antieau, Spherical Witt vectors and integral models for spaces, submitted, [arXiv:2308].

[44] B. Antieau, L. Meier, and V. Stojanoska, Picard sheaves, local Brauer groups, and topological modular forms, to appear in Journal of Topology, [arXiv:2210].

[43] B. Antieau, A. Krause, and T. Nikolaus, The K-theory of Z/p^n – announcement, [arXiv:2204].

[42] B. Antieau, A. Mathew, and M. Morrow, The K-theory of perfectoid rings, Documenta Math. 27 (2022), 1923–1952. [arxiv:2203].

[41] B. Antieau and A. Auel, Explicit descent on elliptic curves and splitting Brauer classes. [arxiv:2106].

[40] B. Antieau, A. Mathew, M. Morrow, and T. Nikolaus, On the Beilinson fiber square, Duke 171 (2022), no. 18, 3707-3806. [arxiv:2003].

[39] B. Antieau and B. Williams, The topological period-index conjecture, Mathematical Research Letters 28 (2021), no. 5, 1307-1317. [arxiv:2003].

[38] B. Antieau and R. Datta, Valuation rings are derived splinters, Math. Z. 299 (2021), 827-851. [Math. Z.]. [arxiv:2002].

[37] B. Antieau and E. Elmanto, Descent for semiorthogonal decompositions, Adv. Math. 380, 26 March 2021. [Advances]. [arxiv:1912].

[36] B. Antieau, B. Bhatt, and A. Mathew, Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p, Forum of Mathematics, Sigma 9:49, 1-26. [Sigma]. [arxiv:1909]. [Video].

[35] B. Antieau and D. Bragg, Derived invariants from topological Hochschild homology, Algebraic Geometry 9 (2022), no. 3, 364-399. [AG]. [arxiv:1906].

[34] N. Addington, B. Antieau, S. Frei, and K. Honigs, Rational points and derived equivalence, Compositio Math. 157 (2021), no. 5, 1036-1050. [Compositio]. [arxiv:1906].

[33] B. Antieau, On the uniqueness of infinity-categorical enhancements of triangulated categories. [arxiv:1812].

[32] B. Antieau and T. Nikolaus, Cartier modules and cyclotomic spectra, J. Amer. Math. Soc. 34 (2021), no. 1, 1-78. [arxiv:1809].

[31] B. Antieau, Periodic cyclic homology and derived de Rham cohomology, Annals of K-Theory 4 (2019), no. 3, 505-519. [arxiv:1808].

[30] B. Antieau and G. Vezzosi, A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XX (2020), 1135-1145. [arxiv:1710]. [Video].

[29] B. Antieau, A. Mathew, and T. Nikolaus, On the Blumberg-Mandell Künneth theorem for TP, Selecta Mathematica, 24 (2018), no. 5, 4555-4576. [Selecta]. [arxiv:1710].

[28] B. Antieau and J. Heller, Some remarks on topological K-theory of dg categories, Proc. Amer. Math. Soc. 146 (2018), 4211-4219. [arxiv:1709].

[27] B. Antieau, A. Auel, C. Ingalls, D. Krashen, and M. Lieblich, Period-index bounds for arithmetic threefolds, Inventiones math. 216 (2019), no. 2, 301-335. [Inventiones]. [arxiv:1704].

[26] B. Antieau, D. Gepner, and J. Heller, K-theoretic obstructions to bounded t-structures, Inventiones math. 216 (2019), no. 1, 241-300. [Inventiones]. [arxiv:1610].

[25] B. Antieau and L. Meier, The Brauer group of the moduli stack of elliptic curves, Algebra & Number Theory 14 (2020), no. 9, 2295-2333. [arxiv:1608], [ANT].

[24] B. Antieau and E. Elmanto, A primer for unstable motivic homotopy theory, Surveys on Recent Developments in Algebraic Geometry, Proc. Sympos. Pure Math. 95 (2017), 305-370. [arxiv:1605].

[23] B. Antieau and B. Williams, Prime decomposition for the index of a Brauer class, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XVII (2017), 277-285. [arxiv:1510].

[22] B. Antieau and G. Stevenson, Derived categories of representations of small categories over commutative noetherian rings, Pacific Journal of Mathematics 283 (2016), no. 1, 21-42. [arxiv:1507].

[21] B. Antieau, On the integral Tate conjecture for finite fields and representation theory, Algebraic Geometry 3 (2016), no. 2, 138-149. [arxiv:1504]. [c2.sage].

[20] B. Antieau, T. Barthel, and D. Gepner, On localization sequences in the algebraic K-theory of ring spectra, Journal of the European Mathematical Society 20 (2018), no. 2, 459-487. [arxiv:1412].

[19] B. Antieau and K. Chan, Maximal orders in unramified central simple algebras, Journal of Algebra 452 (2015), 94-105, [Journal of Algebra]. [arxiv:1412].

[18] B. Antieau, D. Krashen, and M. Ward, Derived categories of torsors for abelian schemes, Adv. Math. 306 (2017), 1-23, [Advances]. [arxiv:1409].

[17] B. Antieau and B. Williams, The prime divisors of the period and index of a Brauer class, J. Pure Apl. Alg. 219 (2015), no. 6, 2218-2224, [JPAA]. [arxiv:1403].

[16] B. Antieau and B. Williams, Topology and purity for torsors, Documenta Math. 20 (2015), 333-355, [Documenta]. [arxiv:1311].

[15] B. Antieau, Twisted derived equivalences for affine schemes, Brauer groups and obstruction problems (Palo Alto, 2013), Progress in mathematics, vol. 320, Birkhauser Basel, 2017, 7-12. [arxiv:1311].

[14] B. Antieau, A reconstruction theorem for abelian categories of twisted sheaves, J. reine angew. Math. 2016 (2016), no. 712, 175–188. [Crelle’s]. [arxiv:1305].

[13] B. Antieau, A local-global principle for the telescope conjecture, Adv. Math. 254 (2014), 280-299, [Advances]. [arxiv:1304].

[12] B. Antieau, Etale twists in noncommutative algebraic geometry and the twisted Brauer space, Journal of Noncommutative Geometry 11 (2017), no. 1, 161-192. [arxiv:1211].

[11] B. Antieau and D. Gepner, Brauer groups and etale cohomology in derived algebraic geometry, Geometry & Topology 18 (2014), no. 2, 1149-1244. [G&T]. [arxiv:1210].

[10] B. Antieau and B. Williams, On the classification of oriented 3-plane bundles over a 6-complex, Topology and its Applications 173 (2014), 91-93. [arxiv:1209].

[9] B. Antieau and B. Williams, Unramified division algebras do not always contain Azumaya maximal orders, Inventiones math. 197 (2014), no. 1, 47-56. [Inventiones]. [arxiv:1209].

[8] B. Antieau and B. Williams, The topological period-index problem over 6-complexes, J. Top. 7 (2014), 617-640. [Journal of Topology]. [arxiv:1208].

[7] B. Antieau and B. Williams, Serre-Godeaux varieties and the etale index, Journal of K-theory 11 (2013), no. 2, 283-295. [arxiv:1205].

[6] B. Antieau, D. Gepner, and J. M. Gomez, Actions of K(pi,n) spaces on K-theory and the uniqueness of twisted K-theory, Trans. Amer. Math. Soc. 366 (2014), no. 7, 3631-3648. [Transactions]. [arxiv:1106].

[5] B. Antieau and B. Williams, The period-index problem for twisted topological K-theory, Geometry & Topology 18 (2014), no. 2, 1115-1148. [G&T]. [arxiv:1104].

[4] B. Antieau, On a theorem of Hazrat and Hoobler, Proc. Amer. Math. Soc. 141 (2013), no. 8, 2609-2613. [arxiv:1104].

[3] B. Antieau, A. Ovchinnikov, and D. Trushin, Galois theory of difference equations with periodic parameters, Comm. Alg. 42 (2014), no. 9, 3902-3943. [arxiv:1009].

[2] B. Antieau, Cech approximation to the Brown-Gersten spectral sequence, Homology, Homotopy and Applications 13 (2011), no. 1, 319-348. [arxiv:0912].

[1] B. Antieau, Cohomological obstruction theory for Brauer classes and the period-index problem, Journal of K-theory 8 (2011), no. 3, 419-435. [arxiv:0909].

thesis

[0] B. Antieau, The spectral index of Brauer classes, PhD thesis (2010), UIC. [pdf].

other writing

[ii] B. Antieau, What is de Rham cohomology?, Oberwolfach Report 35/2022.

[i] B. Antieau, The even filtration after Hahn, Raksit, and Wilson, Oberwolfach Report 24/2022.

current group members and their research

Noah Riggenbach (Boas postdoc).

• Darrell and Riggenbach, TR of quasiregular semiperfect rings is even, [arxiv:2308].
• Riggenbach, K-theory of truncated polynomials, [arxiv:2211].
• Riggenbach, K-theory of cuspidal curves over a perfectoid base and formal analogues, [arxiv:2203].

Carlos Cortez (PhD).

Adam Holeman (PhD).

• Holeman, Derived δ-Rings and relative prismatic cohomology, [arxiv:2303].

Kirill Magidson (PhD).

Deven Manam (PhD).

• Manam, On the Drinfeld formal group, [arxiv:2403].

Yuanning Zhang (PhD).

Anna Lipman (PhD).

Preston Cranford (PhD).

past group members

Xing Gu (UIC PhD 2017).

Victor Jatoba (UIC PhD 2020).

Jānis Lazovskis (UIC PhD 2019).

Tasos Moulinos (UIC PhD 2018).

Harry Smith (UIC PhD 2020).

Joel Stapleton (UIC PhD 2021).

Micah Darrell (NU PhD 2023).

• Darrell and Riggenbach, TR of quasiregular semiperfect rings is even, [arxiv:2308].