Summary
We provide a general algorithm used to prove purity for functors with transfers. As a basic example we consider the Witt group of an algebraic variety.
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Further Reading (Books)
Baeza, R. Quadratic forms over semi-local rings, Lecture Notes in Mathematics, Vol. 655, Springer, Berlin, 1978
Knus, M.-A. Quadratic and Hermitian forms over rings. Grundlehren der Mathematischen Wissenschaften, Vol. 294, Springer, Berlin, 1991
Knus, M.-A., Merkurjev, A., Rost, M., Tignol, J.-P. The Book of Involutions. AMS Colloquium Publications, Vol. 44, AMS, Providence, RI, 1998
Lam, T.Y. The algebraic theory of quadratic forms. Lecture Notes Series, W.A. Benjamin, Reading, MA, 1980
Scharlau, W. Quadratic and Hermitian forms. Grundlehren der Mathematischen Wissenschaften, Vol. 270, Springer, Berlin, 1985
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Zainoulline, K. (2010). Witt Groups of Varieties and the Purity Problem. In: Colliot-Thélène, JL., Garibaldi, S., Sujatha, R., Suresh, V. (eds) Quadratic Forms, Linear Algebraic Groups, and Cohomology. Developments in Mathematics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6211-9_9
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