Chern character for matrix factorizations via Chern–Weil

Given a matrix factorization, we use the Atiyah class to give an algebraic Chern–Weil type construction to its Chern character; this allows us to realize the Chern character in an explicit way. It also generalizes the existing result to any smooth k-algebra Q (k   a commutative ring containing QQ) and any f∈Qf∈Q, which agrees with a recent result of Platt [9]. We also study some basic properties of the Chern character.