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Splittings of truncated motivic Brown--Peterson cooperations algebras
Jackson Morris, Sarah Petersen, Elizabeth Tatum
https://arxiv.org/abs/2509.19542 https://

Splittings of truncated motivic Brown--Peterson cooperations algebras
We construct spectrum-level splittings of $BPGL \langle 1 \rangle \wedge BPGL \langle 1 \rangle$ at all primes $p$, where $BPGL \langle 1 \rangle$ is the first truncated motivic Brown--Peterson spectrum. These are motivic lifts of Mahowald and Kane's splitting of $BP \langle 1 \rangle \wedge BP \langle 1 \rangle$. These splittings are given in terms of motivic Adams covers and constructed over the base fields $\mC, \, \mR,$ and $\mF_q$, where $\textup{char}(\mathbb{F}_q) \neq p$. As an applicat…

Replaced article(s) found for math.KT. https://arxiv.org/list/math.KT/new
[1/1]:
- Splittings of truncated motivic Brown--Peterson cooperations algebras
Jackson Morris, Sarah Petersen, Elizabeth Tatum

Crosslisted article(s) found for math.KT. https://arxiv.org/list/math.KT/new
[1/1]:
- Splittings of truncated motivic Brown--Peterson cooperations algebras
Jackson Morris, Sarah Petersen, Elizabeth Tatum

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Rings of cooperations for Hermitian K-theory over finite fields
Jackson Morris

Rings of cooperations for Hermitian K-theory over finite fields
Jackson Morris
https://arxiv.org/abs/2509.02786 https://arxiv.org/pdf/2509.02786

Rings of cooperations for Hermitian K-theory over finite fields
We compute the ring of cooperations $π_{**}^{\mathbb{F}_q}(\text{kq} \otimes \text{kq})$ for the very effective Hermitian K-theory over all finite fields $\mathbb{F}_q$ where $\text{char}(\mathbb{F}_q) \neq 2.$ To do this, we use the motivic Adams spectral sequence and show that all differentials are determined by the integral motivic cohomology of $\mathbb{F}_q$. As an application, we compute the $E_1$-page of the kq-resolution.