This paper introduces a new approach to the study of certain aspects of
Galois module theory by combining ideas arising from the study of the Galois
structure of torsors of finite group schemes with techniques coming from
relative algebraic $K$-theory.Comment: Final version. To appear in the Proceedings of the London
  Mathematical Societ

Agboola, A.

Burns, D.

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English

On twisted forms and relative algebraic K-theory

Let $M$ be a motive which is defined over a number field and admits an action of a finite dimensional semisimple $\bq$-algebra $A$. We formulate and study a conjecture for the leading coefficient of the Taylor expansion at $0$ of the $A$-equivariant $L$-function of $M$. This conjecture simultaneously generalizes and refines the Tamagawa number conjecture of Bloch, Kato, Fontaine, Perrin-Riou et al. and also the central conjectures of classical Galois module theory as developed by Fröhlich, Chinburg, M. Taylor et al. The precise formulation of our conjecture depends upon the choice of an order $\A$ in $A$ for which there exists a `projective $\A$-structure' on $M$. The existence of such a structure is guaranteed if $\A$ is a maximal order, and also occurs in many natural examples where $\A$ is non-maximal. In each such case the conjecture with respect to a non-maximal order refines the conjecture with respect to a maximal order. We develop a theory of determinant functors for all orders in $A$ by making use of the category of virtual objects introduced by Deligne

Flach, M.

Caltech Authors

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The photo-injector system envisaged for the proposed CLIC linear e+-e- accelerator at CERN has a demanding set of specifications on output pulse structure, power and timing stability. This paper reports on results obtained with quasi-CW diode pumped laser oscillators with output stabilisation. A 300W 804nm diode array stack is used to side pump Nd:YLF (1047nm) crystals with 200μs pulses at 100Hz repetition rate. Using feedback from the laser output to control an acousto-optic loss modulator in the cavity, start-up spiking and Q-switched behaviour is suppressed. Preliminary results obtained on incorporation of a saturable absorbing mirror for passive modelocking are presented

Bente, E.A.J.M.

Valentine, G.J.

University of Strathclyde Institutional Repository

Bente &quot;The photoinjector option for CLIC: past experiments and future developments&quot;,

Control of Q-switched mode locking by active feedback&quot;,

Development of high average power, all-solid-state, passively modelocked neodymium based lasers&quot;

Diode stack supplied by DILAS Diodenlaser, Mainz-Hechtsheim. EY series, microchannel cooled stack

High average power Nd:YVO4 lasers mode locked by strain-compensated saturable Bragg reflectors&quot;,

Stable high repetition rate single frequency Q-switched operation by feedback suppression of relaxation oscillation&quot;,

Investigation into diode pumped modelocked ND based laser oscillators for the CLIC photoinjector system