research

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

publications and preprints

[47] B. Antieau, A. Krause, and T. Nikolaus, On the K-theory of Z/p^n, submitted, [arXiv:2405].

[46] B. Antieau, A. Krause, and T. Nikolaus, Prismatic cohomology relative to $\delta$-rings, submitted, [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, Journal of Topology 17 (2024), no. 2, e12333. [J. Top.]. [arXiv:2210].

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

software

[a] B. Antieau, A. Krause, and T. Nikolaus, KZPN, [GitHub].

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].

Kirill Magidson (PhD).

• Magidson, Divided powers and derived de Rham cohomology, [arXiv:2405].

Deven Manam (PhD).

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

Yuanning Zhang (PhD).

Anna Lipman (PhD).

Preston Cranford (PhD).

past group members

Carlos Cortez (NU PhD 2024).

Adam Holeman (NU PhD 2024).

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

Micah Darrell (NU PhD 2023).

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

Joel Stapleton (UIC PhD 2021).

Harry Smith (UIC PhD 2020).

Tasos Moulinos (UIC PhD 2018).

Jānis Lazovskis (UIC PhD 2019).

Victor Jatoba (UIC PhD 2020).

Xing Gu (UIC PhD 2017).