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Saikat Biswas

Publications and source records attributed to Saikat Biswas.

22 records · Page 2Linked to original sources

ALICE TPC upgrade for High-Rate operations

A new type of Time Projection Chamber (TPC) has been proposed for the upgrade of the ALICE (A Large Ion Collider Experiment at CERN) so as to cater to the high luminosity environment expected at the Large Hadron Collider (LHC) facility in future. This device will rely on the intrinsic ion back flow (IBF) suppression of Micro-Pattern Gas Detectors (MPGD) based technology in particular the Gas Electron Multiplier (GEM). GEM is to minimise the space charge effect in the main drift volume and thus will not require the standard gating grid and the resulting intrinsic dead time. It will thus be possible to read all minimum bias Pb--Pb events that the Large Hadron Collider (LHC) will deliver at the anticipated peak interaction rate of 50 kHz for the high luminosity heavy-ion era in Run 3. New read-out electronics will send the continuous data stream to a new online farm at rates up to 1~TByte/s. The new read-out chambers will consist of stacks of 4 GEM foils combining different hole pitches. In addition to a low ion back flow ($<$ 1\%) other important requirements are good energy resolution (better than 12\% (sigma) for $^{55}$Fe X-rays) and operational stability.

physics.ins-det↗

Tamagawa Torsors of an Abelian Variety

For an abelian variety $A$ over a number field $K$, we define the set of Tamagawa torsors of $A$ at a prime $v$ of $K$ to be the set of principal homogeneous spaces of $A$ over the completion $K_v$ of $K$ at $v$ that are split by an unramified extension of $K_v$. In this paper, we study the arithmetic properties of the Tamagawa torsors.

math.NT↗

Constructing non-trivial elements of the Shafarevich-Tate group of an Abelian Variety over a Number Field

The second part of the Birch and Swinnerton-Dyer (BSD) conjecture gives a conjectural formula for the order of the Shafarevich-Tate group of an elliptic curve in terms of other computable invariants of the curve. Cremona and Mazur initiated a theory that can often be used to verify the BSD conjecture by constructing non-trivial elements of the Shafarevich-Tate group of an elliptic curve by means of the Mordell-Weil group of an ambient curve. In this paper, we generalize Cremona and Mazur's work and give precise conditions under which such a construction can be made for the Shafarevich-Tate group of an abelian variety over a number field. We then give an extension of our general result that provides new theoretical evidence for the BSD conjecture.

math.NT↗