The p-adic height pairing on abelian varieties at non-ordinary primes

In the 80's, P. Schneider constructed the p-adic height pairing on abelian varieties at ordinary primes by using the universal norm group. His construction plays an important role in the proof of the p-adic Gross-Zagier formula at ordinary primes by B. Perrin-Riou. We explain a generalization of Schneider's construction at non-ordinary primes and an application for the p-adic Gross-Zagier formula at non-ordinary primes.