Speaker: Otto Overkamp，Heinrich-Heine-Universität Düsseldorf

Inviter: 黄治中

Title: Unirational algebraic groups and tame ramification

Language: English

Time & Venue: 2026.11.16 16:30-17:30 Zoom Meeting ID: 837 5087 0375 Passcode: 389351

Abstract: Let \Og_K be a complete discrete valuation ring with field of fractions K and algebraically closed residue field k. Let G be an algebraic torus over K. For each d prime to the residue characteristic, let K(d) be the unique extension of K of degree d. I shall report on recent joint work with I. Vanni studying how the Néron lft-model of G behaves under base change to the ring of integers \Og_{K(d)}. Information about this behaviour is encoded in the jumps of Edixhoven’s filtration on the special fibre of the Néron lft-model of G, as well as in Halle-Nicaise’s motivic zeta function of G. In both cases, an important question is whether these objects are rational, was hitherto only known in certain special cases such as tamely ramified tori. I shall give an introduction to these objects and explain a proof that the jumps are indeed rational without any further assumptions on the torus. Time permitting, I shall also indicate how this result generalises to broader classes of commutative algebraic groups.