The mere enumeration of Grothendieck's best known contributions is overwhelming: topological tensor products and nuclear spaces, sheaf cohomology as derived functors, schemes, K-theory and Grothendieck- Riemann -Roch, the emphasis on working relative to a base, defining and constructing geometric objects via the functors they are to represent, fibred categories and descent, stacks, Grothendieck topologies (sites) and topoi, derived categories, formalisms of local and global duality (the 'six operations'), étale cohomology and the cohomological interpretation of L-functions, crystalline cohomology, 'standard conjectures', motives and the 'yoga of weights', tensor categories and motivic Galois groups .
Galos lamang ang baybay ng mga Grothendieck ang pinakamahusay na kilala mga kontribusyon ay napakalaki: topological tensor produkto at nuclear puwang, haya cohomology bilang nagmula functors, pamamaraan, K-teorya at Grothendieck-Riemann-Roch, ang diin sa mga kamag-anak sa isang base, pagtukoy at constructing geometriko bagay sa pamamagitan ng functors sila ay kumakatawan sa, ang himaymay kategorya at pinaggalingan, stack, Grothendieck topologies (site) at topoi, nagmula kategorya, formalisms ng mga lokal at pandaigdigang duality (ang 'anim na operasyon'), étale cohomology at ang cohomological interpretasyon ng L-function, Kristal cohomology, 'standard conjectures', motives at ang' yoga ng mga talaro ', tensor kategorya at motivic Galois grupo.