Up the workers. A travelling French artist takes his cue from rusty biscuit tins, inspirational carpets, a town's forgotten past and trouble at t'mill. By Adrian Searle

With his stacks of old biscuit tins, his photographs of anonymous school kids and murder victims, his mounds of laundry, his lamps and lists of names, Christian Boltanski travels the art world, dragging his litter behind him. One of the few exportable French artists of recent years, his works are an attempt to commemorate the 20th century's depredations: the victims of the holocaust, the "disappeared" of Latin America, murdered innocents. Boltanski has made a career from remembrance; those whom the artist recalls are always spoken for, but never speak; remembered, but never identified.

For the Henry Moore Studio at Dean Clough, Halifax, Boltanski has focused on the history of the site itself. Dean Clough was, until the Thatcher epoch, the largest carpet factory in the world, and John Crossley's mill, which now houses the studio, was, from 1803 until its closure, the largest source of employment in Halifax. Crossley's closed down soon after its purchase by a multinational company, in 1982.

Its soot-blackened exterior scrubbed back to a disconcertingly mellow hue (Heritage Britain always looks like the Cotswolds, even in Halifax), the mill now houses an exhibition studio for international artists. With several galleries and a prize-winning bar/ restaurant that offers Philip Starck seating and indifferent capuccino, there are few visible traces of Dean Clough's history. While the art-trekkies of cosmopolitan Europe and America jet in to see the same artists they go gooey over in Munich and Manhattan, the Henry Moore Sculpture Studio remains a largely unvisited source of wonderment to the locals who, for generations, toiled within its walls.

Taking his cue from the handsomely tooled and gilded volume presented to the retiring director of Crossley's in 1877, which contained the signatures and illiterate crosses of 3,437 employees within its block-printed borders, Boltanski has built a series of stacks of his familiar metal tins, each emblazoned with a worker's name taken from Crossley's retirement roster. The empty tins - all bought new, then artificially rusted and distressed to give them that sombre, wounded-by-time look that has become Boltanski's emblem of soulful portentousness - are arranged in narrow aisles, a tinhenge archive of hollow sentiments.

Down in the basement, behind a steel door, he has set about creating an actual archive of the "lost workers" of Dean Clough (see left). The artist put adverts in local newspapers asking for memorabilia from former employees, which would be placed in an archive for permanent record. Few have so far responded. Mentioning the factory uncovers not just memories, but bitterness and anger. Halifax's economy was destroyed when the mill closed down, and some company pensions have not been honoured. Boltanski's desultory archive, which is being administered by Chris Sacker, contains little: clippings from Crossley's in-house magazine, the odd long-service keepsake certificate, a patch of commemorative carpet.

The last vestige of the local carpet industry is a mill that shreds unwanted clothing down to "shoddy", the fibrous, heterogeneous mulch used for stuffing mattresses and making carpet underlay. Six tons of this material, in varying stages of decomposition, flood the second studio space. While Boltanski's tinned history might be seen as a quasi-minimalist sculpture (a Carl Andre with content) this piece - across which one can trudge, noiselessly, raising a cloud of dust with every step - is a rag colour-field.

Occasionally, an entire garment, a dress or a jacket, can be discerned, like a corpse drowned in dross. Meanwhile, the artist has moved on, to remember someone else he never knew.

n Christian Boltanski is at the Henry Moore Studio, Gate 1, Dean Clough, Halifax (0113 246 7467) to 27 October