Abstract This paper is the first in a series which we offer new framework for hermitian $${\text {K}}$$ K -theory realm of stable $$\infty $$ ∞ -categories. Our perspective yields solutions to variety classical problems involving Grothendieck-Witt groups rings and clarifies behaviour th...

Caution: These polynomials are referred to as w0, w1, w2, ... in Sections 5-8 of [1]. However, beginning with Section 9 of [1], Hazewinkel uses the notations w1, w2, w3, ... for some different polynomials (the so-called big Witt polynomials, defined by formula (9.25) in [1]), which are not the same as our polynomials w1, w2, w3, ... (though they are related to them: in fact, the polynomial wk t...

A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tamely ramified extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt group of graded quadratic forms over the graded ring associated to the filtration defined by the valuation, hence also isomorphic to a direct sum of copies of...

We study the kernel and cokernel of the Frobenius map on the p-typical Witt vectors of a commutative ring, not necessarily of characteristic p. We give many equivalent conditions to surjectivity of the Frobenus map on both finite and infinite length Witt vectors. In particular, surjectivity on finite Witt vectors turns out to be stable under certain integral extensions; this provides a clean fo...

The type of Lasiocampa decolorata (KLUG, 1830), collected in 1820, was successfully barcoded to generate a 658bp COI-fragment after 194 years. The resulting molecular data allowed the description of two closely related species from Morocco: Lasiocampa hannae SPEIDEL, MOOSER & WITT sp. n. from the Anti Atlas and Lasiocampa editae SPEIDEL, MOOSER & WITT sp. n. from the High Atlas.

This presentation describes work undertaken as part of INNOVATE UK funding led by Witt Energy Ltd to investigate the efficacy of a novel design of wave energy converter (WEC). A sealed spherical hull is floating on the surface of the water (Fig. 2(b)) and is moored to the sea bed under a four point catenary mooring system. A mechanical device known as the WITT (Fig. 1) is housed within the hull...

For smooth varieties over finite fields, we prove that the shifted (aka derived) Witt groups of surfaces are finite and the higher GrothendieckWitt groups (aka Hermitian K-theory) of curves are finitely generated. For more general arithmetic schemes, we give conditional results, for example, finite generation of the motivic cohomology groups implies finite generation of the Grothendieck-Witt gr...