{"product_id":"homotopy-theory-of-schemes","title":"Homotopy Theory of Schemes","description":"In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over a reasonable base scheme $k$. He defines the homotopy category $h(\\mathcal{E} k)$ of smooth $k$-schemes and shows that it plays the same role for smooth $k$-schemes as the classical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, for example, concerning the algebraic $K$-theory of those schemes. In this way, advanced methods of algebraic topology become available in modern algebraic geometry.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":57186636530008,"sku":"9780821831649","price":50.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780821831649_88b49006-eff1-4c20-b0c5-8ceef2576842.jpg?v=1780110948","url":"https:\/\/agendabookshop.com\/products\/homotopy-theory-of-schemes","provider":"Agenda Bookshop","version":"1.0","type":"link"}