Tootfinder

On higher regulators of Picard modular surfaces
Linli Shi
https://arxiv.org/abs/2510.08708 https://arxiv.org/pdf/2510.08708

On higher regulators of Picard modular surfaces
We prove the motivic classes in the motivic cohomology groups of Picard modular surfaces with non-trivial coefficients constructed in a paper of Loeffler\textendash Skinner\textendash Zerbes are in the motivic cohomology groups of the interior motives. Then we establish a relation between the motivic classes and non-critical values of the motivic $L$-functions associated to cuspidal automorphic representations of $\mathrm{GU}(2,1)$, thus deducing non-triviality of the motivic classes and provid…

Motivic Homotopy Groups of Spheres and Free Summands of Stably Free Modules
Sebastian Gant, Ben Williams
https://arxiv.org/abs/2510.10033 https://arxiv.org…

Motivic Homotopy Groups of Spheres and Free Summands of Stably Free Modules
Working over an algebraically closed field of characteristic $0$, we show that the motivic stable homotopy groups of the sphere spectrum can be determined entirely from the motivic homotopy groups of the $p$-completed sphere spectra and the motivic cohomology of the ground field, except possibly for the $0$ and $-1$-stems. Using this, we show that the complex realization map from the motivic cohomology group to the classical stable homotopy group is an isomorphism in a range of bidegrees. We ap…

Study: endoscopists used to AI-assisted colonoscopies detected fewer precancerous growths after AI assistance was removed, compared to before AI was introduced (Joedy McCreary/MedPage Today)
https://www.medpagetoday.com/gastroenterology/coloncancer/116968

Relying on AI in Colonoscopies May Erode Clinicians' Skills
Concerns of 'deskilling' raised for clinicians who use AI in colonoscopies, then go without it

Abelian motives and Shimura varieties in nonzero characteristic
James S. Milne
https://arxiv.org/abs/2508.09972 https://arxiv.org/pdf/2508.09972

Abelian motives and Shimura varieties in nonzero characteristic
Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences.

Comcast sues to invalidate a Washington state law that taxes online ad services, set to take effect in October; major ad industry groups also oppose the law (Wendy Davis/MediaPost)
https://www.mediapost.com/publications/article/408…

Comcast Sues Over Washington State Tax On Digital Ads
Comcast has sued to invalidate a new Washington state law that imposes a tax on online advertising services such as creating and placing digital ads, analyzing their performance and planning online campaigns.

Effiziente Perowskit-Solarzellen ersetzen Wegwerf-Batterien in Indoor-Geräten
Modifizierte Perowskit-Solarzellen arbeiten in Innenräumen effizienter und können Kleinelektronik mit Strom versorgen. Wegwerf-Batterien sind dann überflüssig.

$\mathbb{A}^1$-invariant motivic cohomology of schemes
Tom Bachmann, Elden Elmanto, Matthew Morrow
https://arxiv.org/abs/2508.09915 https://arxiv.org/pdf/2…

$\mathbb{A}^1$-invariant motivic cohomology of schemes
Voevodsky outlined a conjectural programme that his slice filtration in motivic homotopy theory should give rise to a good theory of $\mathbb{A}^1$-invariant motivic cohomology. This paper achieves his vision in the generality of arbitrary quasicompact, quasiseparated schemes, by introducing a theory of $\mathbb{A}^1$-invariant motivic cohomology which is related to Weibel's homotopy $K$-theory via an Atiyah--Hirzebruch spectral sequence, and which we compare to étale and syntomic cohomology i…

Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction
Alice Lin
https://arxiv.org/abs/2510.10403 https://arxiv.org/pdf/2510.10403…

Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction
Using integral $p$-adic Hodge theory, Kato and Koshikawa define a generalization of the Faltings height of an abelian variety to motives defined over a number field. Assuming the adelic Mumford-Tate conjecture, we prove a finiteness property for heights in the isogeny class of a motive, where the isogenous motives are not required to be defined over the same number field. This expands on a result of Kisin and Mocz for the Faltings height in isogeny classes of abelian varieties.

Letter: MNG Enterprises, controlled by Alden Global Capital, has upped its offer for The Dallas Morning News by $1 to $17.50/share, $2.50 more than Hearst's bid (Ray Schultz/MediaPost)
https://www.mediapost.com/publications/art…

Alden Global Capital Unit Raises Offer For 'The Dallas Morning News'
Alden's MNG Enterprises is now offering $17.50 per share, increasing its bid by $1.

Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers
Yoshiaki Okumura
https://arxiv.org/abs/2508.08692 https://arxiv.org/pdf/2508…

Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers
For rank-two $A$-motives defined over local fields with odd characteristic, we give an analogue of a theorem of Imai stating that abelian varieties with good reduction over $p$-adic fields have only finitely many torsion points values in cyclotomic towers. This implies the finiteness of torsion points of abelian Anderson $A$-modules. For rank-two Drinfeld $A$-modules over global function fields, we also give an analogue of a theorem of Ribet on torsion points of abelian varieties values in maxi…