Who is responsible for the creation of Earth, Lord Shiva or Adhishakti?
Lord Shiva can not create alone without the help of Adi Shakti. This is the essence of various scriptures.
Adi Shankaracharya's Soundarya Lahiri mentions this at the very beginning:
Shivah shakthya yukto yadi bhavati shaktah prabhavitum
Na chedevam devo na khalu kusalah spanditumapi;
Atas tvam aradhyam Hari-Hara-Virinchadibhir api
Pranantum stotum vaa katham akrta-punyah prabhavati
Lord Shiva, only becomes able. To do creation in this world. along with Shakthi Without her, Even an inch he cannot move, And so how can, one who does not do good deeds, Or one who does not sing your praise, Become adequate to worship you Oh , goddess mine, Who is worshipped by the trinity.
However, in Hinduism we have the concept of the Trinity - Brahma (creator), Vishnu (preserver) and Mahesawra (destroyer). So, usually creation comes under Lord Brahma's duties.